GIFT  OF 
ENGINEERING  LIBRARY 


ALTERNATING  CURRENTS  OF 
ELECTRICITY : 


THEIR 


Generation,  Measurement,  Distribution, 
and  Application. 

AUTHORIZED    AMERICAN   EDITION. 


BY 


GISBERT    KAPP,    C.E., 

MEMBER  OF  THE  INSTITUTION  OF  CIVIL  ENGINEERS  ; 
MEMBER  OF  THE  INSTITUTION  OF  ELECTRICAL  ENGINEERS. 


WITH   AN    INTRODUCTION 

BY 

WILLIAM   STANLEY,   JR. 


NEW   YORK: 

THE   W.  J.   JOHNSTON   COMPANY,  LTD., 

41  PARK  Row  (TIMES  BUILDING). 

1893. 


Reprinted  from  Professional  Papers  of  the  Corps  of  Royal 
Engineers,  by  permission  of  the  Committee  of  the  R.  E.  Insti- 
tute, and  with  the  consent  of  the  author. 


GIFT  OF 


LIBRARY 


INTRODUCTION. 


THE  writings  of  Mr.  Kapp  have  always  interested 
American  engineers.  In  fact,  whenever  a  new 
branch  of  our  science  develops  into  attractive  im- 
portance and  requires  "treatment,"  we  expect  that 
Mr.  Kapp  will  place  the  matter  before  us  in  simple 
terms  and  illustrate  the  points  of  interest  by  exam- 
ples possessing  practical  importance.  The  follow- 
ing pages  accord  with  the  previous  writings  of  Mr. 
Kapp  in  this  respect. 

Starting  with  the  assumption  that  the  reader  is 
acquainted  with  the  behavior  of  steady  currents  in 
circuits  whose  constants  are  readily  obtainable,  he 
proceeds  to  explain  the  growth  of  a  periodic  cur- 
rent, and  in  so  doing  beguiles  the  student  into 

865686 


4  INTRODUCTION. 

mastering  a  few  simple  mathematical  methods,  a 
knowledge  of  which  is  fundamentally  necessary. 

As  the  volume  advances  its  scope  becomes  appar- 
ent, for  it  treats  in  a  simple  and  yet  effective  man- 
ner of  periodic  currents  in  general,  of  the  phase 
relations  of  impressed  and  induced  E.  M.  F's  pos- 
sible in  simple  circuits,  of  Alternators  (somewhat 
in  detail),  of  the  requirements  of  Central  Stations 
(briefly),  of  Alternating  Current  Motors,  and  finally 
of  Multiphase  Currents.  One  does  not  expect  ex- 
haustive treatment  of  any  one  of  these  subjects 
within  the  compass  of  a  small  book. 

From  an  educational  standpoint  Chapters  I.  and 
II.  are  of  especial  importance.  These  forty 
pages  might  well  be  increased  fourfold,  for  al- 
though they  contain  a  summary  of  the  elemental 
knowledge  necessary  for  a  correct  understanding  of 
the  principles  operating  alternating  currents  in 
simple  circuits,  possessing  resistance  and  self- 
induction,  they  do  not  treat  of  capacity  effects  and 
the  problems  incident  thereto.  In  Chapter  IV.  we 
have  some  of  the  formulae  for  calculating  induced 


INTRODUCTION.  5 

E.  M.  F.s  (whether  occurring  in  alternators  or  in 
transformers)  with  constants  for  particular  cases  of 
armature  coils.  Chapter  V.  is  devoted  to  Machine 
Construction,  and  points  out  the  dependence  of 
efficiency  on  core  wastes,  giving  a  curve  of  the 
relation  of  watts  per  ton  of  core  metal  lost  by 
hysteresis,  to  the  induction  density.  Chapter  VI. 
is  devoted  to  transformers  and  briefly  points  out 
the  necessity  for  careful  design  in  this,  the  simplest 
of  alternate  current  apparatus.  The  chapters  on 
Central  Stations  are  of  interest,  as  they  not  only 
describe  a  few  English  plants,  but  also  give  us  the 
author's  criticisms  on  various  distribution  methods. 
The  chapters  on  Alternate  Current  Motors  and  Mul- 
tiphase Currents  complete  the  little  volume. 

There  are  one  or  two  opinions  expressed  by  the 
author  to  which  exceptions  may  be  taken,  notably 
the  statement  on  page  143  that  the  resultant  field 
produced  by  quarter-phase  currents  varies  40$,  and 
that  the  Dobrowolski-Tesla  arrangement  of  three 
phased  currents  produces  a  shifting  field  of  more 
constant  value  than  the  quarter-phased  or  two- 


6  INTRODUCTION. 

phased  arrangement.  For  a  discussion  of  these 
points  the  reader  may  consult  The  Electrical  World, 
vol.  xix.,  p.  249,  Kelly;  vol.  xx.,  p.  4,  Dolivo- 
Dobrowolski;  p.  36,  Kelly,  Steinmetz;  p.  114,  C. 
E.  L.  Brown. 

In  general,  however,  Mr.  Kapp's  statements  are 
clear,  true,  and  convincing,  and  are  of  interest  and 
value  to  every  American  engineer. 

WM.  STANLEY,  JR. 


CONTENTS. 


CHAPTER 

I. — INTRODUCTORY,       .        .        .  •  •        •      9 

II.— MEASUREMENT  OF  PRESSURE,  CURRENT,  AND  POWER,     .     37 

APPENDICES,          .        .      ,.     '    • ~^«  •    44 

III.— CONDITION  OF  MAXIMUM  POWER,   .        .        .        .        -49 

APPENDIX,     .        *     ^.."  ,   .        .        •        •        •         •     5& 

IV.— ALTERNATING  CURRENT  MACHINES,        .        .        •        •     5& 

V.— MECHANICAL  CONSTRUCTION  OF  ALTERNATORS,  .     73 

VI. — DESCRIPTION  OF  SOME  ALTERNATORS,      .        .        .        .     82 

VII. — TRANSFORMERS,       .        .  • 

VIII.— CENTRAL  STATIONS  AND  DISTRIBUTION  OF  ALTERNATING 

CURRENTS,  '.  •        •        •        •        •  -  '  •  I05 

IX.— EXAMPLES  OF  CENTRAL  STATIONS,  .        ,        .        •        •  XI7 

X. PARALLEL  COUPLING  OF  ALTERNATORS,  .        .        -        .123 

XI.— ALTERNATING  CURRENT  MOTORS, I26 

XII.— SELF-STARTING  MOTORS, I36 

XIII.— MULTIPHASE  CURRENTS,          .        •        •       .•        •        •  I4° 


Alternating  Currents  of  Electricity: 


THEIR 


GENERATION,    MEASUREMENT,    DISTRIBUTION, 
AND    APPLICATION. 


CHAPTER    I. 

INTRODUCTORY. 

WHEN  we  think  or  speak  of  electric  currents  we 
are  accustomed  to  regard  them  in  the  light  of  ma- 
terial currents,  of  something  which  flows  along  a 
path  formed  by  the  conductor,  and  has,  therefore, 
a  direction.  We  say  that  electricity  flows  along 
the  conductor  or  through  the  conductor  from  the 
place  of  higher  to  that  of  lower  potential;  in  the 
same  way  that  water  will  flow  from ,  the  higher  to 
the  lower  level  through  a  pipe.  Such  a  view  is,  of 
course,  purely  conventional.  As  a  matter  of  fact 
we  do  not  know  whether  it  is  the  positive  electric- 

9 


10  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

ity  that  flows  ip.  ta:  given  direction,  or  the  negative 
electricity  that^febws  in  the  opposite  direction,  or 
,l<ynbth^r  ^bot&  electricities  flow  simultaneously  in 
opposite  directions,  or  whether  there  is  any  trans- 
fer of  electricity  through  the  wire  at  all.  Indeed, 
according  to  modern  views,  there  is  merely  transfer 
of  energy,. but  not  through  the  wire,  the  transfer 
taking  place  throughout  the  space  surrounding  the 
wire.  To  talk  about  an  electric  current  flowing 
through  a  wire  may  therefore  be  an  unscientific 
way  of  expressing  our  meaning,  but  it  is  a  very 
convenient  way,  and,  therefore,  generally  adopted. 
Now  in  adopting  this  conception  of  the  flow  of  a 
certain  thing  called  electricity  along  a  predescribed 
path,  we  have  also  adopted  the  idea  that  this  flow 
takes  place  in  a  direction  which  is  perfectly  well 
defined  in  each  given  case.  We  have  no  sense  by 
which  we  can  directly  perceive  an  electric  current 
or  note  its  direction.  It  is  true  that  if  we  get  a 
shock  we  are  made  aware  that  a  current  has  passed 
through  us,  but  no  number  of  shocks  will  help  a 
man  in  the  slightest  degree  to  an  understanding  of 
the  real  nature  of  electric  currents,  nor  enable  him 
to  determine  their  direction.  We  must  be  content 


INTRODUCTORY.  II 

to  study,  not  the  currents  themselves,  but  their 
chemical,  thermic,  magnetic,  and  mechanical  ef- 
fects. Amongst  other  things  we  must  also  deter- 
mine the  direction  of  current  by  one  or  other  of 
these  effects.  For  instance,  we  know  that  a  wire 
stretched  north-south  over  a  compass  needle,  and 
carrying  a  current,  will  deflect  the  needle.  If  the 
north-seeking  end  is  deflected  to  the  left  or  west- 
ward, we  know  by  Ampere's  rule  that  the  current 
flows  from  south  to  north.  Conversely,  if  the  de- 
flection is  in  the  opposite  sense,  we  conclude  that 
the  current  is  from  north  to  south.  If  the  current 
is  obtained  from  a  battery  without  the  intervention 
of  any  piece  of  moving  apparatus,  such  as  a  revers- 
ing key,  we  notice  that  the  needle  once  deflected 
remains  in  that  position  as  long  as  the  current 
flows,  and  we  naturally  conclude  that  the  current 
flows  continuously  in  the  same  direction,  that  it 
is,  in  fact,  a  "  continuous  "  current.  Now  suppose 
you  were  to  notice  that  the  needle,  after  remaining 
deflected  to  the  left  for  a  certain  time,  were  to 
swing  over  to  the  right  and  to  remain  deflected  in 
that  position  an  equal  time,  then  again  swing  to 
the  left,  and  so  take  alternately  these  two  opposite 


12  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

positions,  you  would  immediately  conclude  that 
someone  had  put  a  reversing  key  into  your  circuit, 
and  was  amusing  himself  by  working  it  at  regular 
intervals.  The  behaviour  of  the  needle  would,  in 
fact,  have  shown  you  that  you  have  no  longer  to 
do  with  a  continuous  current,  but  that  your  current 
has  become  an  alternating  current,  that  is,  a  cur- 
rent which  changes  its  direction  periodically.  You 
will  notice  that  I  have  assumed  that  the  needle  has 
time  to  follow  each  impulse  of  the  current,  in  other 
words,  that  the  periodic  time  of  the  current  is  large 
in  comparison  with  the  time  of  oscillation  of  the 
needle.  Suppose,  however,  that  I  were  to  work  the 
reversing  key  so  fast  that  the  needle  cannot  fol- 
low the  different  impulses ;  in  this  case  it  will,  of 
course,  remain  in  its  north-south  position,  and  will 
have  become  useless  as  an  instrument  for  the  de- 
tection of  an  alternating  current.  We  require  an 
apparatus  which  will  respond  far  more  readily  than 
a  sluggish  compass  needle  to  the  different  current 
impulses  which  follow  each  other  with  great  rapid- 
ity. To  get  such  an  apparatus,  let  us  take  an  iron 
diaphragm,  and  hold  near  the  centre  of  it  a  coil  of 
insulated  wire  forming  part  of  the  circuit,  or  bet- 


INTRODUCTORY.  13 

ter  still,  an  electromagnet  with  a  laminated  core; 
why  the  core  should  be  laminated  I  shall  explain 
later  on.  For  the  present  it  interests  us  to  note 
that  the  poles  must  be  in  such  a  position  that  at 
least  one  of  them  may  act  on  the  diaphragm. 
Thus  a  ring-shaped  magnet  which  has  no  free 
poles  would  not  serve  our  purpose ;  a  straight  bar 
magnet,  however,  will  do  well.  Now  observe  what 
happens  if  an  alternating  current  is  sent  through 
the  coil  of  this  magnet.  At  the  moment  of  press- 
ing down  the  key  to  complete  the  circuit  the  bat- 
tery begins  to  send  a  continuous  current  through 
the  coil  and  the  core  begins  to  get  magnetized. 
The  magnetization  grows  from  zero  to  a  maximum, 
and  retains  that  value  until  the  key  is  lifted  again, 
when  it  falls  to  zero.  Now  reverse  the  current  and 
go  through  the  same  process.  It  is  obvious  that  at 
each  reversal  of  the  current  the  magnetization  must 
pass  through  zero,  and  the  end  of  the  core  which 
is  presented  to  the  diaphragm  will  alternately  be- 
come a  north  and  south  pole.  The  diaphragm  will, 
therefore,  be  alternately  attracted  and  released,  or, 
in  other  words,  it  will  vibrate,  and  if  the  period  of 
vibration  is  quick  enough,  that  is,  if  I  manipu- 


14  ALTERNATING    CURRENTS   OF   ELECTRICITY. 

late  the  reversing  key  very  rapidly,  a  musical  note 
may  be  produced.  Conversely,  if  I  approach  an 
electromagnet  to  a  diaphragm  and  find  that  the 
latter  is  not  permanently  attracted,  but  is  set  in 
vibration  and  emits  a  musical  note,  then  I  conclude 
that  the  current  which  flows  through  the  coil  of  the 
electromagnet  is  an  alternating  current,  and  the 
rapidity  of  the  alternations,  or,  as  it  is  called, 
the  "frequency"  of  the  current,  can  be  judged 
from  the  pitch  of  the  note.  In  explaining  this 
experiment  I  have,  for  the  sake  of  simplicity,  as- 
sumed that  the  current  is  furnished  by  a  battery, 
and  that  its  alternating  character  is  produced  by 
means  of  a  reversing  key.  This  mechanism  is, 
however,  not  an  essential  part  of  the  experiment  or 
of  its  explanation.  The  essential  part  is  that  the 
current  shall  grow  from  zero  to  a  maximum,  and 
diminish  again  to  zero,  then  change  its  direction 
and  grow  to  a  negative  maximum,  diminish  to 
zero,  then  become  positive  again,  and  so  on.  Such 
a  current  is  produced  by  a  certain  class  of  electric 
machines  called  "alternators,"  which  will  occupy 
us  a  good  deal  during  this  lecture.  But  before  en- 
tering into  this  subject  I  wish  to  show  you  experi- 


INTRODUCTORY.  15 

mentally  the  fact  that  an  alternating  current  can 
produce  these  oscillating  or  wave-like  magnetic 
effects  which  I  described  a  moment  ago.  The  ap- 
paratus I  shall  use  in  my  illustrations  is  extremely 
simple.  I  have  here  a  small  electromagnet  of  the 
kind  used  in  connecting  arc  lamps  to  alternating 
current  circuits,  and  which  is  technically  termed  a 
"  choking  coil."  For  a  diaphragm  I  use  the  bottom 
of  an  ordinary  biscuit  tin,  and  you  will  observe  that 
when  I  approach  one  end  of  the  choking  coil  to  the 
biscuit  tin  there  is  emitted  a  sound  which  can  be 
heard  all  over  the  room.  The  sound  is  not  exactly 
a  clear  musical  note,  because,  as  might  have  been 
expected  in  a  rough-and-ready  apparatus  of  this 
kind,  the  elasticity  of  the  diaphragm  is  by  no 
means  perfect.  But  such  as  the  sound  is,  it  serves 
quite  well  to  show  that  the  diaphragm  is  set  vibrat- 
ing by  the  current,  and,  in  fact,  every  telephone 
receiver  exemplifies  the  same  action. 

The  study  of  alternating  currents  is  greatly  facil- 
itated by  a  rational  and  simple  manner  of  repre- 
senting them  graphically.  There  are  various  ways 
in  which  we  can  so  represent  not  only  alternating 
currents,  but  any  quantity  which  varies  periodi- 


10  ALTERNATING   CURRENTS   OF   ELECTRICITY. 

cally.  The  most  obvious  way  of  representing  an 
alternating  current  is  by  drawing  a  curve,  the  two 
co-ordinates  of  which  represent  time  and  the  in- 
stantaneous current  strength.  In  Fig.  i  the  time 


FIG.  i. 

is  measured  on  the  horizontal,  and  the  current 
strength  on  the  vertical.  We  thus  obtain  a  wavy 
line  which  cuts  at  regular  intervals  through  the 
axis  of  abscissae.  These  are  the  points  of  reversal 
when  the  current  strength  is  maximum,  positive 
where  the  line  lies  above,  and  negative  where  it 
lies  below  the  axis.  The  exact  shape  of  the  curve 
depends  on  the  construction  of  the  machine  which 
produces  the  alternating  current;  but  I  may  at 
once  say  that  in  nearly  all  the  theoretical  investi- 
gations of  alternating  currents  it  is  assumed  that 
the  curve  follows,  or  rather  represents,  a  sine  func- 


INTRODUCTORY.  1 7 

tion,  and  that  this  assumption  is  sufficiently  near 
the  truth  for  all  practical  purposes.  All  of  you 
know,  of  course,  what  a  sinusoidal  curve  is,  and  I 
need,  therefore,  not  explain  it  at  length.  As,  how- 
ever, the  way  of  plotting  a  sinusoidal  curve  brings 
me  to  a  second  method  of  representing  an  alternat- 
ing current  graphically,  I  must  say  a  few  words 
about  it.  Imagine  yourself  standing  some  distance 
in  front  of  a  steam  engine  in  a  line  with  the  axis  of 
the  cylinder,  and  looking  at  the  crank  pin.  The 
latter  will  then  appear  to  be  moving  up  and  down, 
making  equal  excursions  to  both  sides  of  the  cen- 
tre of  the  crank  shaft.  You  will,  in  fact,  see  the 
projection  of  the  crank  on  a  vertical,  and  the  length 
of  this  projection  at  any  instant  is  equal  to  the 
length  of  the  crank  multiplied  with  the  sine  of  the 
angle  which  the  crank  makes  at  that  instant  with 
the  horizontal.  The  angle  is,  of  course,  the  pro- 
duct of  the  angular  velocity  and  the  time;  and 
since  the  angular  velocity  is  constant,  you  will  also 
obtain  a  sine  curve  by  plotting  the  time  on  the  hori- 
zontal and  the  projection  of  the  crank  on  the  verti- 
cal. The  curve  I  in  Fig.  i  has  been  so  obtained. 
We  may,  however,  save  ourselves  the  trouble  of 


i8 


ALTERNATING   CURRENTS   OF   ELECTRICITY. 


plotting  this  curve,  for  we  can  represent  the  alter- 
nating current  more  directly  by  the  projection  on 
the  vertical  of  a  line  OI  (Fig.  2)  revolving  with  a 
constant  angular  speed  round  the  fixed  centre  O. 

The  length  of  OI  represents  to  any  convenient 
scale  the  maximum  value  of  the  current,  or  the 
crest  of  the  current  wave,  and  its  projection  repre- 
sents its  instantaneous  value.  You  see  that  for 


FIG.  2. 

half  a  revolution  this  value  is  positive,  and  for  the 
other  half  of  the  revolution  it  is  negative. 

In  this  diagram,  which  is  called  a  "clock  dia- 
gram," we  must  therefore  make  a  projection  in 
order  to  find  the  instantaneous  value  of  the  current. 
This  is  less  laborious  than  the  plotting  of  a  sine 
curve,  but  it  is  possible  to  represent  the  current  in 


INTRODUCTORY.         .  19 

a  still  more  simple  way.  Those  of  you  who  are 
familiar  with  Zeuner's  valve  diagram  will  immedi- 
ately see  how  this  can  be  done.  Instead  of  draw- 
ing the  circle  round  O  as  centre,  we  draw  it  passing 
through  O.  The  diameter  of  this  circle  (Fig.  3) 


O 


FIG.  3. 

represents  to  any  convenient  scale  the  maximum 
value  of  the  current.  Then  the  instantaneous  cur- 
rent is  given  directly  by  the  length  of  the  revolv- 
ing line  between  O  and  the  circle.  To  obtain  the 
negative  values  of  the  current,  we  reproduce  the 
circle  on  the  opposite  side;  this  in  the  figure  is 
shown  dotted. 

To  illustrate  the  use  of  any  of  these  graphic 
methods  of  representing  alternating  currents,  let 
us  suppose  that  we  have  to  solve  the  following 
problem : — We  have  an  iron  core  wound  with  two 
independent  coils,  each  carrying  an  alternating 


20  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

current.  The  two  currents  shall  have  the  same 
frequency,  that  is  to  say,  the  time  which  elapses 
between  two  succeeding  positive  maxima  or  nega- 
tive maxima  shall  be  the  same  for  both  currents, 
but  the  maxima  in  the  two  currents  shall  not  occur 
at  the  same  moment.  In  other  words,  the  phase 
of  one  current  shall  lag  behind  that  of  the  other, 
just  as  in  a  two-cylinder  steam  engine  one  crank 
lags  behind  the  other.  Now  the  problem  we  have 
to  solve  is :  what  will  be  the  magnetization  of  the 
core  at  any  instant?  To  find  this  we  must  of 
course  know  the  instantaneous  value  of  the  excit- 
ing power,  or  the  ampere  turns  resulting  from  the 
action  of  both  currents  combined ;  we  must,  in  fact, 
find  what  resultant  current  acting  alone  will  have 
the  same  effect  as  the  two  given  currents  acting 
together.  Let,  in  Fig.  i,  the  curves  I  and  II  rep- 
resent the  two  currents,  or  better  still  the  ampere 
turns  of  these  currents,  then  the  ampere  turns  of 
the  resultant  current  are  found  by  plotting  the 
algebraical  sum  of  the  ordinates.  Thus  we  obtain 
curve  III.  It  is  self-evident,  and  needs,  therefore, 
no  elaborate  proof,  that  this  curve  can  also  be 
obtained  from  Fig.  2  if  in  that  figure  we  draw  a 


INTRODUCTORY. 


21 


parallelogram  of  currents  (precisely  in  the  same 
way  as  in  mechanics  we  draw  a  parallelogram  of 
forces),  and  use  the  resultant  O  III  to  plot  the  sine 
curve.  You  see  that  we  can  combine  currents  in  the 
same  way  as  mechanical  forces.  I  have  proved  this 
for  the  case  that  the  currents  flow  in  two  independ- 
ent coils,  but  a  glance  at  Fig.  4  will  show  you  that  it 


D 

FIG.  4. 

also  holds  good  if  the  two  currents  are  sent  through 
the  same  coil.  Here  we  have  two  machines,  Ai 
and  A2,  mechanically  coupled,  and  therefore  pro- 
ducing currents  of  the  same  frequency.  These 
currents,  I  and  II,  flow  into  one  circuit  containing 
a  coil  C.  It  is  evident  that  in  the  circuit  BCD 
there  flows  only  one  current,  which  is  the  algebraic 
sum  of  I  and  II. 

Now  let  us   change   the   arrangement   to    that 


22  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

shown  in  Fig.  5.  Here  we  have  to  do  with  only  a 
single  current,  for  both  machines  and  coil  C  are 
coupled  in  series ;  but  we  have  to  do  with  two  elec- 


FIG.  5. 

tromotive  forces,  namely,  those  of  the  machines. 
I  assume  that  the  coil  C  in  itself  has  no  electromo- 
tive force.  In  this  case  also  it  is  self-evident  that 
the  current  which  will  be  forced  through  C  is  due 
to  the  algebraic  sum  of  the  two  electromotive 
forces,  and  that  all  I  have  said  about  the  determi- 
nation of  the  resultant  current  is  directly  applicable 
to  that  of  the  resultant  electromotive  force.  In 
other  words,  we  may  use  any  of  the  three  graphic 
methods  of  representing  currents  also  for  represent- 
ing electromotive  forces. 

These  graphic  methods  of  investigation,  and  es- 
pecially those  based  on  the  clock  diagram,  are  so 


INTRODUCTORY.  23 

useful  and  so  simple  that  I  shall  employ  them  fre- 
quently in  the  course  of  these  lectures  in  preference 
to  analytical  methods,  and  it  is  therefore  expedient 
to  familiarize  you  at  the  outset  with  the  clock  dia- 
gram. For  this  purpose  I  select,  by  way  of  exam- 
ple, a  case  which  is  very  frequently  met  with,  and 
which  is  represented  by  Fig.  6.  Lest  you  should 


FIG.  6. 

think  that  this  case  has  merely  theoretical  impor- 
tance, I  may  at  once  say  that  a  certain  deduction 
which  flows  naturally  from  its  consideration  is  of 
great  practical  importance  in  motors  driven  by 
multiphase  currents,  since  on  it  depends  the  start- 
ing torque  of  such  motors.  If  you  compare  Figs. 
5  and  6  you  will  find  that  they  only  differ  in  this : 
that  an  electromagnet  S  has  been  substituted  for  the 
machine  A2.  The  circuit  represented  in  Fig.  6 


24  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

consists  of  a  machine  A,  giving  an  alternating  elec- 
tromotive force,  a  resistance  B,  consisting  of  a 
bank  of  glow  lamps,  and  an  electromagnet  S.  This 
electromagnet  has  a  property  which  is  technically 
called  "self-induction/'  and,  before  going  further, 
I  must  briefly  explain  to  you  what  is  meant  by 
self-induction.  You  know  that  an  electromotive 
force  is  set  up  in  a  wire  whenever  the  wire  cuts 
across  magnetic  lines  of  force.  Since  the  wire 
must  necessarily  form  part  of  a  closed  circuit  (for 
if  the  circuit  were  not  closed  there  could  be  no  cur- 
rent), the  cutting  of  lines  must  be  accompanied  by 
an  increase  or  decrease  in  the  number  of  lines  or 
total  induction  threading  through  the  circuit,  and 
we  may  therefore  also  say  that  whenever  the  total 
induction  through  a  circuit  changes,  there  is  an 
electromotive  force  set  up  in  the  circuit  which  is 
the  greater  the  more  rapid  the  change.  In  fact, 
the  rate  of  change,  that  is,  number  of  lines  added 
or  withdrawn  per  second,  multiplied  with  the  num- 
ber of  turns  of  wire,  gives  the  electromotive  force 
set  up  in  the  coil.  Going  back  to  Fig.  i,  we  have 
seen  that  the  curve  I  represents  the  current  as  a 
function  of  the  time.  Suppose  there  is  no  other 


INTRODUCTORY.  25 

coil  wound  over  the  core,  then  the  ordinates  of  the 
curve  represent  to  a  suitable  scale  also  the  exciting 
power  on  the  core,  and  it  is  obvious  that  the  mag- 
netization of  the  core,  or,  to  speak  correctly,  the 
total  induction  passing  through  it,  will  change 
more  or  less  in  accordance  with  the  curve  I.  If 
the  permeability  were  constant,  the  induction  would 
be  strictly  proportional  to  the  exciting  power,  and 
by  the  selection  of  a  suitable  scale  the  curve  repre- 
senting induction  could  be  made  to  coincide  with 
the  current  curve  I.  Now  for  low  values  of  the 
induction,  say  between  zero  and  3,000  or  4,000 
lines  per  square  centimetre,  we  may  regard  the 
permeability  of  soft,  well-annealed  wrought-iron  as 
approximately  constant,  and  if  we  do  not  press  the 
induction  beyond  this  point,  we  may  without  any 
great  error  assume  that  the  current  curve  I  also 
represents  the  total  induction  through  the  core. 
For  the  points  where  the  current  passes  through 
zero,  and  which  momentarily  interest  us  the  most, 
the  assumption  is,  of  course,  quite  correct.  But  if 
the  curve  I  represents  the  total  induction,  then  the 
geometrical  tangent  to  it  at  any  point  represents 
the  change  of  induction  in  unit  time,  or,  as  I  said 


26  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

just  now,  the  rate  of  change  of  induction  at  the  par- 
ticular moment  represented  by  the  point  on  the 
curve.  Thus,  reading  off  the  time  on  the  horizon- 
tal axis,  we  can,  by  drawing  the  tangent  to  the 
current  curve  at  the  corresponding  points,  find  the 
rate  at  which  the  total  induction  changes  at  each 
moment.  I  said  just  now  that  the  rate  of  change, 
multiplied  with  the  number  of  turns  in  the  coil, 
gives  the  electromotive  force  generated  at  any  in- 
stant in  the  coil,  and  it  will  now  be  clear  to  you 
that  this  electromotive  force,  which  we  call  the 
"electromotive  force  of  self-induction,"  must  be 
proportional  to  the  geometrical  tangent  to  the  cur- 
rent curve.  The  steeper  this  line,  the  greater  is 
the  electromotive  force.  Thus  you  see  that  when 
the  current  is  either  a  positive  or  negative  maxi- 
mum, the  tangent  is  horizontal,  and  therefore  at 
those  moments  the  electromotive  force  of  self- 
induction  is  zero.  On  either  side  of  maximum  cur- 
rent it  has  a  definite  value,  but  this  value  is  posi- 
tive on  one  side  and  negative  on  the  other  side  of 
maximum  current,  since  the  slope  of  the  tangent 
changes  from  upward  to  downward  when  passing 
this  point.  Where  the  current  curve  intersects  the 


INTRODUCTORY.  27 

horizontal  axis,  the  slope  of  the  tangent  is  evi- 
dently greatest,  and  we  therefore  see  that  the  elec- 
tromotive force  of  self-induction  is  a  maximum 
when  the  current  passes  through  zero,  and  it  is 
itself  zero  when  the  current  is  a  maximum.  This 
then  is,  in  general  terms,  the  relation  between  the 
current  curve  and  the  curve  giving  the  electromo- 
tive force  of  self-induction.  It  remains  yet  to  de- 
termine the  exact  nature  of  the  latter.  We  have 
seen  that  the  ordinates  of  the  electromotive  force 
curve  are  proportional  to  the  geometric  tangent 
drawn  to  the  current  curve.  Now  how  do  we  draw 
the  tangent  to  the  point  A  for  instance  ?  We  draw 
a  straight  line  through  this  point,  and  one  very 
near  it,  on  the  current  curve.  To  speak  correctly, 
I  should  say  infinitely  near  it.  At  this  infinitely 
near  point  the  current  will  have  increased  from  i  to 
i  -f  di,  and  the  time  from  t  to  t  -f-  dt.  The  ratio  of 
di  to  dt  is  therefore  equal  to  the  geometrical  tangent 
at  A.  But  this  ratio  is  the  differential  quotient  of 
the  current  in  respect  to  time,  and  we  thus  find 
that  the  curve  giving  the  electromotive  force  of 
self-induction  is  the  first  differential  of  the  current 
curve. 


28  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

I  have  up  to  the  present  entirely  avoided  the  use 
of  mathematics,  but  now  it  becomes  necessary  to 
introduce  a  few  simple  formulae.  Going  back  to 
Fig.  2,  suppose  that  the  radius  OI,  the  projection 
of  which  gives  the  instantaneous  value  of  the  cur- 
rent, makes  n  complete  revolutions  per  second.  Its 
angular  speed  is  then  o>  =  2itn,  and  its  angular 
position  at  the  time  t  is  a  =  W,  counting  the  time 
from  the  moment  that  the  radius  is  horizontal. 
Let  I  be  the  length  of  the  radius,  which  also  repre- 
sents the  maximum  of  the  current  strength,  or  crest 
of  the  wave,  then  the  instantaneous  value  of  the 
current  at  the  time  /  is 

/  =  I  sin  tot (i), 

and  the  electromotive  force  of  self-induction  at  that 
moment  is 

ea  —  Lwl  cos  wt (2), 

L  being  a  coefficient  which  depends  on  the  perme- 
ability of  the  core,  the  magnetic  reluctance  of  the 
whole  magnetic  circuit,  and  the  number  of  turns  in 
the  coil.  At  the  time  when  the  current  passes 
through  zero  we  get  the  maximum  value  of  the 
electromotive  force,  which  is 

E.  =  L«I (3), 


INTRODUCTORY.  29 

and  we  can  also  write  the  equation  for  the  instan- 
taneous value  of  the  electromotive  force  of  self- 
induction  in  the  form 

ea  =  E8  cos  w/, 
or 

ea  =  -  E8  sin  (  ut  -  - ) (4), 


from  which  you  will  see  that  this  value  may  also  be 
graphically  represented  by  a  sine  curve,  but  lag- 
ging behind  the  current  curve  by  90  degrees.  To 
obtain  the  electromotive  force  curve,  which  is 
shown  dotted  in  Fig.  7,  we  must  therefore  imagine 


a  crank  OE8  rigidly  attached  to  the  crank  OI  (Fig. 
8)  at  an  angle  of  90  degrees,  and  we  must  plot  the 
projections  of  this  second  crank  on  the  vertical  as 
ordinates  in  Fig.  7.  A  study  of  this  diagram  (Fig. 
7)  will  help  you  materially  to  an  understanding  of 


30  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

the  phenomena  of  self-induction.  As  time  pro- 
gresses, from  left  to  right  you  see  that  at  first  the 
current  is  positive  and  increases.  But  self-induc- 
tion opposes  the  increase,  and  its  electromotive 
force  is  therefore  negative.  The  dotted  curve  is 
below  the  axis.  This  opposition  becomes  fainter 
as  the  current  approaches  its  maximum  value,  since 
the  rate  of  change  of  the  induction  becomes  less 
and  less.  When  the  current  has  reached  its  posi- 
tive maximum,  the  rate  of  change  has  become  zero, 
and  the  opposition  of  self-induction  has  vanished. 
The  dotted  curve  passes  through  the  axis.  A 
moment  later,  the  current  is  still  positive,  but  is 
now  decreasing.  Again  self-induction  opposes  the 
change ;  its  tendency  is  to  keep  the  current  up  at 
its  maximum  strength.  The  electromotive  force 
of  self-induction  tries  to  push  on  the  current ;  it  is 
positive,  and  the  dotted  curve  rises  above  the 
horizontal.  This  tendency  to  push  on  the  current 
increases  until  the  current  has  become  zero,  and 
begins  to  flow  in  the  reverse  direction.  The  nega- 
tive current  is  now  opposed  by  the  positive  electro- 
motive force  of  self-induction,  but  the  opposition 
grows  fainter  as  the  current  grows  stronger,  and  so 


INTRODUCTORY.  3! 

the  see-saw  of  pushing  on  and  checking  back  the 
current  is  kept  up. 

The  point  which  interests  us  most  is  what  must 
be  the  electromotive  force  given  by  the  machine  A, 
in  Fig.  6,  to  produce  the  current  shown  by  the 
curve  in  Fig.  7.  To  simplify  our  investigation  we 
shall  assume  that  the  ohmic  resistance  of  the  coil 
S  and  machine  A  is  negligible  in  comparison  with 
the  ohmic  resistance  of  the  bank  of  lamps  B,  or 
that  it  is  included  therein ;  also  that  the  only  part 
of  the  circuit  having  self-induction  is  the  coil  S. 
Then  it  is  immediately  obvious  that  a  voltmeter 
placed  across  the  terminals  of  this  coil  will  indicate 
the  electromotive  force  of  self-induction,  and  a 
voltmeter  placed  across  the  lamps  will  indicate  the 
electromotive  force  corresponding  to  the  product  of 
current  and  the  resistance  of  the  bank  of  lamps. 
But  it  is  not  immediately  obvious  that  the  sum  of 
these  two  readings  will  give  us  the  electromotive 
force  as  measured  by  a  voltmeter  across  the  ter- 
minals of  the  machine,  and  I  will  show  you  pres- 
ently, by  theory  and  by  experiment,  that  this  is 
not  the  case.  Assuming  the  resistance  of  the  bank 
of  lamps  to  be  a  fixed  quantity  r,  it  is  clear  that  the 


32  ALTERNATING    CURRENTS   OF   ELECTRICITY. 

instantaneous  lamp  volts  equal  the  product  r  X  /, 
and  that  they  can  be  represented  by  a  sine  curve  er 
of  the  same  phase  as  the  current  curve.  In  Fig.  8 


FIG.  8. 

the  radius  of  maximum  lamp  volts  OEr  must  there- 
fore coincide  with  the  radius  of  maximum  current 
OI.  The  radius  of  maximum  volts  of  self-induc- 
tion is  OE8,  and  this,  as  I  have  already  shown,  lags 
behind  the  current  radius  by  90  degrees.  To  find 
the  machine  volts  at  any  instant,  we  must  combine 
the  curves  er  and  es,  but  remember  to  take  the  lat- 
ter with  the  opposite  sign,  for  the  self-induction 
opposes  the  current.  This  gives  us  the  curve  e  in 
Fig.  7.  To  find  the  machine  volts  from  Fig.  8  we 
have  to  draw  a  radius  of  such  length  and  position 
that  it  may  be  regarded  as  the  resultant  of  the  lamp 


INTRODUCTORY,  33 

volts  Er,  and  an  electromotive  force  diametrically 
opposed  to  that  of  self-induction.  We  prolong, 
therefore,  the  line  E8O  beyond  O,  and  make  OE/  = 
OE8.  Completing  the  parallelogram,  we  thus  find 
the  resultant  OE,  which  gives  us  the  maximum 
machine  volts,  or  "impressed  electromotive  force." 
The  diagram  (Fig.  8)  is  very  instructive.  In  the 
first  place,  it  enables  us  at  once  to  find  an  expres- 
sion for  the  angle  of  lag  <f>.  You  see  that  the  tan- 
gent of  this  angle  is  given  by  the  ratio  of  the  elec- 
tromotive force  of  self-induction  to  that  usefully 
expended  over  the  lamps.  I  must  here  remark 
that  when  I  speak  of  electromotive  force  and  cur- 
rent I  mean,  for  the  present,  always  their  maxi- 
mum values.  Retaining  the  notation  previously 
employed,  we  have,  therefore — 

tan  <p  = 


rl  ' 
tan?  =     -~ (5). 


Next  we  can  find  an  expression  for  the  current  as 
a  function  of  the  impressed  electromotive  force  and 
the  constants  of  the  circuit.     Since  the   triangle 
OE.E  is  rectangular,  we  have 
3 


34  ALTERNATING   CURRENTS   OF   ELECTRICITY. 

E3  =  Era  +  E8a, 

or,  with  our  previous  notation — 
E2  =  r2P  +  L2«/T, 

E 


(s-). 


If  we  had  to  do  with  a  continuous  current,  its  equa- 

•p* 
tion  would  be  I  =  —     Since   the   term   under   the 

r 

square  root  must,  under  all  circumstances,  be  larger 
than  unity,  the  current  produced  by  an  alternating 
electromotive  force  must  always  be  smaller  than  the 
current  which  an  equal  but  continuous  electromo- 
tive force  would  produce  in  the  same  circuit. 

The  term  ^/r"  -\-  L/V  is  called  the  "  impedance  " 
of  the  circuit,  and  Lw  its  "inductance."  As  an  aid 
to  memory,  I  reproduce  in  Fig.  9  Dr.  Fleming's 
diagram,  in  which  these  terms  are  recorded.  You 
have  seen  that  Ohm's  law  is  not  applicable  to  alter- 
nate current  circuits,  but  if  we  substitute  the  im- 
pedance for  the  ohmic  resistance,  this  law  becomes 
applicable. 


INTRODUCTORY.  35 

I  have  yet  to  explain  the  meaning  of  the  quantity 
which  we  called  L,  and  which  we  introduced  in 
order  to  take  account  of  the  number  of  turns  in  the 
coil,  and  other  properties  of  the  circuit.  Of  course, 
most  of  you  will  long  ago  have  recognized  in  this 
L  the  usual  coefficient  of  self-induction,  but,  for 


the  sake  of  completeness,  I  must  prove  this.  There 
are  various  definitions  for  the  coefficient  of  self- 
induction,  but  the  following  will  serve  my  pur- 
pose :  —  "  The  coefficient  of  self-induction  is  the  ratio 
between  the  counter  electromotive  force  in  any  cir- 
cuit and  the  time  rate  of  variation  of  the  current 
producing  it."  *  In  symbols  — 


Sumpner,  The  Variation  of  Coefficients  of  Induction.    Phil. 
..June,  1887,  p.  453. 


36  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

and  substituting  i  from  equation  (i),  we  have— 
e8  =  Latl  cos  iot    (2), 

which  is  identical  with  equation  (2) ,  and  shows  that 
the  L  we  then  introduced  is  indeed  the  coefficient 
of  self-induction. 


CHAPTER   II. 

MEASUREMENT   OF  PRESSURE,    CURRENT,    AND 
POWER. 

When  showing  you  the  last  experiment,  I  had 
occasion  to  use  a  voltmeter,  and  the  question  we 
have  now  to  consider  is  what  is  the  relation  be- 
tween the  reading  of  the  instrument  and  the  maxi- 
mum electromotive  force  in  the  circuit.  That  the 
reading  must  be  less  than  the  true  maximum  is 
obvious,  but  less  by  how  much? 

To  answer  this  question  we  may  use  the  analyti- 
cal or  the  geometric  method.  I  give  the  former  in 
Appendix  I.  of  this  chapter  and  the  latter,  which  is 
due  to  Mr.  Blakesley,  in  Fig.  10.  A  Cardew  volt- 
meter measures  not  directly  volts,  but  simply  the 
amount  of  heat  developed  in  its  wire  per  unit  of  time. 
The  rate  at  which  heat  is  developed  at  any  instant 
is  the  product  of  the  instantaneous  current  and  the 
instantaneous  volts;  but  as  the  current  passing 

37 


38  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

through  the  wire  is  proportional  to  the  volts,  the 
rate  at  which  heat  is  developed  is  proportional  to 
the  square  of  the  instantaneous  volts,  that  is,  to  Oe 
squared  in  Fig.  10,  if  by  OE  we  represent  the  max- 
imum volts.  Now,  to  find  the  general  effect  of  a 
large  number  of  succeeding  instantaneous  voltages 
on  the  voltmeter,  we  have  to  draw  the  projections 
Oe  of  OE  for  a  large  number  of  positions.  Let  us 
take  these  positions  in  pairs,  such  as  OE  and  OE', 
with  an  angular  interval  of  90  degrees  between 


FIG.  10. 

them.  It  is  evident  that  for  such  pair  the  sum  of 
the  squares  of  the  projections  is  equal  to  the  square 
of  the  maximum  voltage,  and  that  the  mean  vol- 
tage is  y2  Ea.  This  is  independent  of  the  actual 
position  of  each  pair,  and  is,  therefore,  the  mean 
value  of  all  the  possible  pairs.  The  volts  read  on 


MEASUREMENT    OF    PRESSURE,   CURRENT,   AND    POWER.    39 

the  Cardew  (or  any  other  instrument,  the  action  of 
which  depends  on  the  square  of  the  voltage)  must 
therefore  be  multiplied  by  the  square  root  of  2  in 
order  to  get  the  maximum  volts  ;  or  in  symbols,  if 
by  e  we  represent  the  volts  shown  by  the  instru- 
ment, and  by  E  the  maximum  volts  — 

E 
*  =  ~r  ....................  (7)< 

A/2 

At  the  Paris  Congress,  in  1889,  it  has  been  decided 
to  call  e  the  "  effective  "  volts. 

The  same  reasoning  which  I  have  here  applied 
to  the  measurement  of  pressure  can  also  be  applied 
to  the  measurement  of  current,  provided  that  the 
measuring  instrument  is  of  a  kind  in  which  the 
movable  part  is  subjected  to  a  force  varying  as 
the  square  of  the  current.  Thus  a  Siemens'  dyna- 
mometer, a  Thomson  ampere-balance,  and  similar 
instruments,  will  indicate  the  "  effective  current  "  — 

'•=4=  ...................  («)• 

A/2 


It  is  important  to  osberve  that  this  is  not  the  same 
thing  as  the  mean  or  average  current.  To  under- 
stand the  distinction,  let  us  first  settle  what  quan- 


40  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

tity  we  call  the  mean  current.  Imagine  an  alter- 
nating current  commutated  each  time  it  passes 
through  zero,  and  let  the  unidirected  but  pulsating 
current  thus  obtained  pass  through  an  electrolytic 
apparatus,  say,  for  instance,  a  copper  voltmeter. 
The  weight  of  copper  thrown  down  in  unit  time  is 
a  measure  of  the  "  mean  strength  "  of  our  pulsating 
current.  The  mean  current  strength  thus  defined 
is  about  90  per  cent,  of  the  effective  current 
strength,  so  that  to  get  the  true  mean  current  we 
must  multiply  the  reading  of  the  Siemens'  dyna- 
mometer byf  90.  The  proof  for  this  is  given  in  Ap- 
pendix II.  of  this  chapter. 

We  have  seen  that  the  measurement  of  pressure 
and  current  is  a  very  simple  matter ;  but  the  meas- 
urement of  power,  to  which  I  must  next  draw  your 
attention,  is  not  quite  so  simple  as  with  continuous 
currents.  You  know  that  if  we  wish  to  determine 
the  power  given  to  a  circuit  by  a  continuous  cur- 
rent we  have  merely  to  observe  the  amperes  and 
the  volts,  and  multiply  them  to  get  the  watts.  If 
we  divide  the  watts  by  746,  we  get  the  result  in 
horse-power.  With  alternating  currents  this  is  not 
quite  so  simple,  and  if  we  were  to  compute  the 


MEASUREMENT    OF    PRESSURE,   CURRENT,   AND    POWER.     41 

power  in  this  manner,  our  results  would  be  gen- 
erally too  large,  and  never  too  small.  The  reason, 
of  course,  is  that  the  instant  of  maximum  amperes 
does  generally  not  coincide  with  the  instant  of 
maximum  volts.  To  get  the  true  power  we  must 
integrate  the  product  of  the  instantaneous  volts 
and  amperes  over  a  complete  cycle,  and  divide  by 
the  time  required  to  perform  the  complete  cycle. 
The  matter  is  treated  analytically  in  Appendix  III. 
of  this  chapter,  while  here  I  treat  it  graphically, 


FIG.  ii. 

using  again  Mr.  Blakesley's  method.  In  Fig.  1 1 
OE  and  OI  represent  electromotive  force  and  cur- 
rent at  any  given  moment,  OE'  and  OI'  their 
position  a  quarter  period  later.  The  current  lags 
behind  the  electromotive  force  by  the  angle  <?. 


42  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

Using  small  letters  for  the  projections  of  E  and  I 
on  the  vertical,  the  mean  value  of  the  power  for 
the  two  positions  is  obviously  ei  -\-  e'i'  -f-  2. 

From  the  diagram,  the  following  equations  are 
obvious : — 

ei  =  EI  sin  a  sin  /?. 
e'i'  =  EI  cos  a  cos  /?. 

Combining  these  we  find  the  mean  power — 

•py 
w  =  -'-  (cos  a  cos  /9  -j-  sin  a  sin  £). 

EI 

W  =  —   COS  (a  -  /3). 

EI 
a/  =  —  cos  <p    (9), 

and  this  is  the  same  for  every  pair  the  position  of 
which  differs  by  90  degrees.  It  is,  therefore,  the 
true  equivalent  power. 

•p  T 

Since  e  =  — —  and  /  =  — — ,  we  have  also — 

V2  V2 

w  =  ei  cos  <p (10), 

where  e  and  i  are  the  volt  and  ampere  readings,  as 
obtained  by  our  usual  instruments. 

You  see  we  have  first  to  determine  the  "  appar- 


MEASUREMENT    OF    PRESSURE,   CURRENT,   AND    POWER.     43 

ent "  watts  as  if  we  had  to  do  with  a  continuous 
current,  and  then  to  get  the  true  watts  we  must 
multiply  by  the  cosine  of  the  angle  of  lag.  It  is, 
however,  not  always  easy  to  determine  the  angle  of 
lag,  and  to  avoid  the  labour  and  possible  errors  of 
such  a  determination,  various  instruments  have 
been  invented  for  the  direct  measurement  of  power, 
which  are  called  wattmeters.  The  best-known 
form  of  wattmeter  is  constructed  similarly  to  a  Sie- 
mens' dynamometer.  The  fixed  coil,  containing  a 
few  turns  of  thick  wire,  is  connected  in  series  with 
the  main  circuit,  and  the  movable  or  suspended 
coil,  containing  many  turns  of  fine  wire,  is  con- 
nected as  a  shunt  to  the  main  circuit.  A  non- 
inductive  resistance  is  put  in  circuit  with  the  mov- 
able coil  to  reduce  the  self-induction  of  the  shunt 
circuit.  (For  theory  of  wattmeter,  and  corrections 
to  be  applied,  see  Appendix  IV.,  following.) 


44  ALTERNATING    CURRENTS   OF    ELECTRICITY, 


APPENDIX     I. 


Voltmeter  absorbs  in  time  T  the  energy  — 

/"V 
-dt. 
r 


sin2  (a>t)  d  ( 
r     Q  \    /      \. 


i?! 

a)  r 


2    r 

And  since 


w  =  — » 
r 


E 
= 


MEASUREMENT    OF   PRESSURE,  CURRENT,   AND    POWER.    45 

APPENDIX   II. 


Mean  current,  as  determined  by  electrolysis,  is  cou- 
lombs divided  by  time— 

T 


Ut    =.    7T. 

2 


Mean  current — 

C   =   7^-    /   *    i». 


t  =  I  sin  (•/)  A 


2 

The  effective  current  is — 

I 


46  ALTERNATING   CURRENTS   OF   ELECTRICITY. 

therefore 


or  very  nearly 

c  =  0*9  /. 


APPENDIX   III. 


Work  done  by  current  during  one  cycle  is  wT,  and 
per  second  it  is  — 


i    /»T 

=  =  I        etdt. 
1  «/o 


IE     /»27r     , 
w  =  ;7p  /         Sin  a  sin  (a  4-  y)  da. 


W   ~~   ~27tJo  27r°OS  ^  S^n'  "^   +   S^n  ^  S^n  a  COS  a^a- 

lEr        /«    i  x  /T 

=  ilT  LCOS  ^  vl  ~  ~  sm  a  cos  a  j-f  sin  ^  I  -^ sin8  a 

IE  r  -i  IE 

w  ==  — r  I  cos  ^     or  w  =  —  cos  «>  or  «/  =  /V  cos  <P 

27T     |_  2 


MEASUREMENT    OF   PRESSURE,  CURRENT,  AND   POWER.    47 


APPENDIX   IV. 


Let  <f>  be  the  angle  of  lag  in  the  circuit,  the  power 
given  to  which  is  to  be  measured,  and  let  d  be  the  angle 
of  lag  in  the  fine  wire  coil  of  the  wattmeter,  due  to  its 
self-induction.  Let  I  be  the  current  through  the  thick 
wire  coil,  and  /  the  current  through  the  fine  wire  coil, 
then  the  power  indicated  by  the  wattmeter,  if  the  cur- 
rents were  steady,  would  be  Kri  I  where  K  is  the  co- 
efficient of  the  instrument,  and  r  the  resistance  of  the 
fine  wire  coil.  The  true  watts  of  the  alternating  cur- 
rent of  E  volts  are — 

W  =  IE  cos  <p. 
The  indicated  watts  are — 

W  =  K  (Reading). 

W  =  K>/  cos  (<p  -  d)  I  =  KE  cos  d  cos  (<f>-  3)  I. 

Therefore,  to  get  true  watts,  we  must  multiply  the 
watts  indicated  by 

cos  <f> 

cos  d  cos     >  -  8 


48  ALTERNATING   CURRENTS   OF   ELECTRICITY. 

which  expression  can  also  be  written  in  the  form — 

i  +  tanM 
i  +  tan  3  tan  <p  ' 

If  the  wattmeter  has  no  self-induction,  d  =  o,  and  no 
correction  is  required.  Again,  if  the  self-induction  of 
the  wattmeter  is  equal  to  that  of  the  circuit  to  be 
measured — 

,      i  +  tan8  d 

tan  d  =:  tan  0,  and  — ; — ' =  i. 

i  -f  tan  d  tan  <p 

In  this  case  also  no  correction  is  required.  In  all 
other  cases  the  corrections  given  in  this  formula  must 
be  applied. 


CHAPTER    III. 

CONDITION   OF    MAXIMUM    POWER. 

It  is  important  to  investigate  the  conditions 
under  which  we  can  obtain  a  maximum  of  power 
in  a  given  circuit.  This  is  the  deduction  of  which 
I  have  spoken  a  little  while  ago  as  flowing  natu- 
rally from  the  investigation  of  the  case  represented 
by  Fig.  6.  Here  we  have  an  alternating  current 
machine,  a  self-induction,  and  a  bank  of  lamps. 
The  self-induction  we  cannot  diminish,  and  the 
machine  volts  we  cannot  increase.  How  must  we 
manage  our  lamps  to  get  a  maximum  of  power  into 
them,  and  therefore  to  get  a  maximum  of  light  out 
of  them?  Without  entering  into  any  lengthy 
mathematical  investigation,  you  can  see  at  once 
that  the  ohmic  resistance  of  the  bank  of  lamps  will 
have  a  great  deal  to  do  with  the  amount  of  power 
usefully  expended.  If  the  resistance  is  very  high, 
the  lamps  will  get  very  nearly  the  whole  of  the 
4  49 


50  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

machine  volts,  but  then  the  current  will  be  small. 
If,  on  the  other  hand,  we  lower  the  resistance  too 
much  in  our  desire  to  get  a  large  current,  we  shall 
have  to  sacrifice  nearly  the  whole  of  the  pressure, 
since  the  self-induction,  which  now  is  fed  by  a 
large  current,  will  choke  back  most  of  the  available 
voltage.  You  see  that  either  too  little  or  too  much" 
resistance  is  bad,  and  we  have  to  find  that  resist- 
ance which  will  give  us  the  best  effect.  This  will 
be  the  case  when  the  volts  over  the  lamps  equal 
the  volts  over  the  self-induction,  either  being  about 
70  per  cent,  of  the  machine  volts.  I  give  the  ana- 
lytical proof  in  an  appendix  to  this  chapter  and  the 
geometric  proof  by  means  of  the  clock  diagram 
(Fig.  12).  Let,  in  this  figure,  the  circle  represent 
the  given  machine  volts,  and  let  OE8  be  the  volts 
of  self-induction  corresponding  to  the  current  OI. 
Then  the  tangent  of  the  angle  at  I  is  obviously  equal 
to  Lw  (by  equation  (3)).  The  power  given  to  the 
lamps  is  (by  equation  (9))  w  =  J^  IE  cos  ?,  that  is, 
the  projection  of  the  volt  radius  on  the  current 
radius,  multiplied  by  the  current,  and  divided  by  2. 
But  the  projection  of  the  machine  volts  OE  gives 
us  the  lamp  volts  OEr  and  the  current  is  proper- 


CONDITION    OF   MAXIMUM    POWER.  51 

tional  to  the  volts  of  self-induction  (see  triangle 
OIES),  so  that  we  can  also  say  the  power  is  propor- 
tional to  the  product  of  lamp  volts  and  self-induc- 
tion volts  (that  is,  to  the  shaded  area  in  Fig.  12), 


FIG.  12. 

and  our  problem  can  also  be  stated  in  these  terms  :  — 
Find  that  position  of  OE  for  which  the  shaded 
area  becomes  a  maximum.  Obviously  this  will  be 
the  case  when  the  line  OE  forms  an  angle  of  45  de- 
grees with  the  horizontal;  in  other  words,  when 
the  current  lags  by  one-eighth  of  a  period  behind 
the  impressed  electromotive  force,  and  when  the 
volts  measured  over  the  self-induction  equal  the 
lamp  volts.  This  condition  will  be  fulfilled  when 
the  resistance  of  the  bank  of  lamps  is 


r  = 


52  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

In  order  to  simplify  the  explanation,  I  have  as- 
sumed that  in  Fig.  6  the  resistance,  the  self-induc- 
tion, and  the  seat  or  source  of  electromotive  force, 
are  different  and  distinct  parts  of  the  circuit.  This 
was,  however,  not  essential.  We  could,  for  in- 
stance, assume  the  self-induction  to  be  part  and 
parcel  of  the  machine,  or  even  of  the  bank  of 
lamps,  and  yet  our  result  would  have  been  the 
same.  Nay,  more.  Suppose  we  take  away  the 
lamps  and  put  in  their  place  a  series  wound  dynamo 
with  well-laminated  field  magnets.  Whichever  way 
the  current  is  sent  through  the  machine  it  will  al- 
ways revolve  in  the  same  direction,  and  the  alter- 
nating current  must,  therefore,  set  it  in  motion. 
Now,  imagine  the  period  of  the  current  very  long, 
in  fact,  so  long  that  the  electromotive  force  of  self- 
induction  of  the  magnet  coils  and  armature  may  be 
neglected.  Then  the  only  force  opposing  the  cur- 
rent in  its  flow  through  the  armature  is  the  counter 
electromotive  force  developed  by  the  latter,  which, 
at  constant  speed  of  rotation,  is  proportional  to  the 
field  strength.  Now,  if  we  do  not  excite  the  mag- 
nets strongly  (and  on  account  of  hysteresis  and 
other  losses  it  is  advisable  to  work  with  a  low  in- 


CONDITION    OF    MAXIMUM    POWER.  53 

duction) ,  we  may  consider  the  field  strength  to  be 
proportional  to  the  current,  so  that  the  only  force 
which  opposes  the  current  will  in  this  case  be  at  all 
times  proportional  to  the  current  strength.  It  will, 
in  fact,  be  the  same  kind  of  opposition  as  is  pro- 
duced by  ohmic  resistance,  but  with  this  difference, 
that,  instead  of  converting  the  electric  power  into 
heat  in  the  lamps,  we  convert  it  into  mechanical 
power,  which  may  be  taken  off  the  spindle  of  the 
motor.  So  far  the  motor,  although  supplied  with 
an  alternating  current  of  very  long  period,  will 
work  exactly  as  if  it  were  joined  to  a  continuous 
current  circuit.  But  now  let  us  increase  the  fre- 
quency of  a  current,  that  is  to  say,  let  us  shorten 
the  period  and  have  more  and  more  current  waves 
per  second.  This  will  add  to  the  counter  electro- 
motive force  of  the  motor  (which  is  useful,  because 
accompanied  by  the  giving  out  of  mechanical 
power)  another  electromotive  force  which  is  en- 
tirely useless,  namely,  the  electromotive  force  of 
self-induction.  This  must  considerably  decrease 
the  power  obtainable  from  the  motor,  first,  because 
the  current  strength  has  been  decreased  by  its 
action ;  and,  secondly,  because  with  the  electromo- 


54  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

live  force  of  self-induction  now  having  become  a 
large  quantity,  a  considerable  lag  of  the  current 
behind  the  machine  volts  must  take  place.  A  few 
years  ago  I  experimented  with  a  motor  of  this 
kind,  and  found  that  the  power  obtainable  from  the 
machine  when  coupled  to  an  alternating  current 
circuit  was  only  about  one-sixth  its  normal  power 
on  a  continuous  current  circuit.  In  this  motor  the 
self-induction  was  far  too  large  as  compared  with 
its  counter  electromotive  force.  By  our  rule,  the 
electromotive  force  of  self-induction  should  have 
been  equal  to  the  counter  electromotive  force. 
In  this  case  the  motor  would  give  about  70  per 
cent,  of  the  power  it  could  develop  with  a  contin- 
uous current.  If  it  were  possible  to  make  motors 
which  fulfill  the  condition  I  have  explained,  it 
would  be  a  very  easy  and  practical  solution  of  the 
problem  how  to  make  the  existing  lighting  stations 
which  supply  alternating  current  available  for  the 
distribution  of  power;  but  I  doubt  very  much  the 
possibility .  of  this  solution  of  the  problem.  The 
self-induction  of  such  a  motor  must  always  be  enor- 
mously high,  but  a  way  in  which  we  can  at  least 
approach  the  best  condition  of  working  is  by  lower- 


CONDITION    OF    MAXIMUM    POWER:  55 

ing  the  frequency  and  increasing  the  rotary  speed 
of  the  motor.  I  have  devoted  some  time  to  this 
method  of  working  alternate  current  motors,  be- 
cause it  has  already  acquired  practical  importance, 
not  indeed  in  the  regular  working  of  these  ma- 
chines, but  in  the  starting  of  them.  The  Ganz 
motor  is  started  without  a  load,  as  if  it  were  an 
ordinary  continuous  current  machine,  and  after  it 
has  acquired  a  certain  speed  it  suddenly  begins  to 
work  as  an  alternating  current  machine.  When  in 
this  condition  the  load  can  be  thrown  on,  and  the 
machine  will  eVen  stand  a  certain  amount  of  ex- 
cess load. 


56  ALTERNATING    CURRENTS    OF   ELECTRICITY. 


APPENDIX. 


The  power  is  w  =  ^  IE  cos  y,  or  substituting  for  cos 
the  value  — »  and  for  I  the  value 


Vs       <*aLa  Vr* 


we  have  also  — 


w  =  w       • 

^   i" 

r 

The  variable  is  r,  and  to  find  for  which  value  of  r 
the  power  w  becomes   a   maximum,   we  resolve  the 

equation  —  =•  o,  and  find  r  =  wL,  and  the  maximum 
power — 

i  E' 

w  =  \  —  » 

fc    r 

or,  if  by  e  we  represent  the  effective  voltage,  such  as 
would  be  indicated  on  a  Cardew  voltmeter,  we  have 

also — r 

e* 

w  =  —  • 


CONDITION    OF    MAXIMUM    POWER.  57 

The  analogy  with  the  well-known  rule  for  maxi- 
mum power  from  a  source  of  continuous  current  is  re- 
markable. According  to  this  rule,  maximum  power 
will  be  developed  in  the  external  circuit,  if  its  resist- 
ance is  equal  to  the  resistance  of  the  battery  or  machine 
which  gives  the  current.  If  E  is  the  electromotive 
force  of  the  battery,  and  r  its  internal  resistance,  the 
maximum  power  which  is  obtainable  in  an  external 
circuit  of  equal  resistance  is — 

iE2 

w  = > 

4   r 

precisely  the  same  expression  as  obtained  above  for  al- 
ternating currents. 


CHAPTER   IV. 

ALTERNATING   CURRENT   MACHINES. 

When  discussing  the  electromotive  force  of  self- 
induction,  we  have  seen  that  this  is  produced  by  the 
change  in  the  total  induction  passing  through  the 
electric  circuit,  or,  which  comes  to  the  same  thing, 
by  the  cutting  of  wires  across  magnetic  lines  of 
force.  In  a  choking  coil  the  magnetization  changes, 
and  we  thus  obtain  an  electromotive  force  without 
the  necessity  of  moving  the  wire;  but  when  the 
strength  of  the  field  is  a  constant,  and  its  position 
in  space  remains  the  same,  then  we  must  move  the 
wire  in  order  to  get  an  electromotive  force,  and 
this  is  precisely  what  we  do  in  our  alternating  cur- 
rent machines  or  "alternators."  The  most  simple 
conceivable  form  of  alternator  is  shown  in  Fig.  13. 
Here  we  make  use  of  the  vertical  component  of  the 
earth's  magnetic  field,  and  the  electromotive  force 

is  a  maximum  when  the  wire  is  either  at  its  high- 

58 


ALTERNATING    CURRENT    MACHINES. 


59 


est  or  lowest  position  (crank  vertical),  and  when 
the  wire  is  in  the  extreme  right  or  left  position 
(crank  horizontal)  the  electromotive  force  is  zero. 
The  apparatus  shown  in  Fig.  13  is,  in  fact,  simply 


t  >    FIG.  13. 

a  mechanical  model  of  the  clock  diagram.  In  this 
figure  the  bearings  and  standards  supporting  them 
are  represented  as  forming  the  terminals ;  and  wires 
attached  to  them  as  shown,  and  led  to  a  solenoidal 
electromagnet,  will  energize  the  latter.  Provided 
the  strength  of  the  field  were  sufficiently  great,  we 
could,  when  the  crank  is  rapidly  rotated  by  a  cord 
and  pulley,  produce  with  the  electromagnet  the 
effects  I  have  shown  you  when  the  coil  was  con- 
nected to  a  transformer.  But  the  strength  of  the 
field  provided  by  the  earth  is  not  nearly  sufficient. 


60  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

We  must  resort  to  an  artificial  field  produced  by 
electromagnets,  such,  for  instance,  as  is  shown 
in  Fig.  14,  where  NS  are  the  polar  surfaces  of  two 
electromagnets,  between  which  a  coil  C  is  rotated. 
If  the  polar  surfaces  extend  some  distance  beyond 
the  diameter  D  of  the  coil,  we  may  assume  that  the 
field  within  the  space  swept  by  the  coil  is  uniform, 
and  then  the  number  of  lines  or  total  induction 


s 
FIG.  14. 

passing  through  the  coil  at  any  instant  will  be  pro- 
portional to  the  sine  of  the  angle  the  coil  forms 
with  the  vertical.  The  electromotive  force  will 
then  be  proportional  to  the  sine  of  the  angle  the 
coil  forms  with  the  horizontal.  Calling  H  the  field 
intensity,  /  the  length  of  the  coil,  v  the  velocity, 
and  r  the  number  of  wires  counted  on  both  sides, 


ALTERNATING   CURRENT   MACHINES.  6l 

the  maximum  electromotive  force  in  C.G.S.  meas- 
ure, when  the  coil  is  vertical,  will  be 

Hztfr. 

It  is  convenient  to  introduce  instead  of  H,  the 
number  of  lines  per  square  centimetre,  the  total 
induction  F  passing  through  the  coil  ;  and  instead 
of  the  linear  velocity,  the  number  of  revolutions 
per  second,  which,  in  this  case,  where  we  have  to 
do  with  a  two-pole  machine,  is  equal  to  the  fre- 
quency n.  A  simple  algebraical  operation,  which 
need  not  be  reproduced,  here  gives  us  the  following 
formula  for  the  maximum  electromotive  force  :  — 

E  =  27tnF  -. 

2 

The  effective  electromotive  force  is  obtained  by 
dividing  this  expression  by  the  square  root  of  two, 
and  if  we  wish  to  get  the  electromotive  force  in 
volts  we  multiply  by  10  to  the  power  of  minus  8, 
or  in  symbols  — 


e  =  2  -22,  Fr#  io"8  ................  (n). 

Now  suppose  we  remove  the  armature  shown  in 
Fig.  14,  and  replace  it  by  one  wound  to  give  a 


62  ALTERNATING    CURRENTS  OF   ELECTRICITY. 

continuous  current.  We  use  the  same  total  length 
of  wire,  but  spread  the  turns  evenly  all  round  the 
circle  and  put  on  a  commutator.  As  you  know,  the 
electromotive  force  of  this  machine  will  now  be 

e  —  Yrn  io"8. 

The  current  flows  through  the  armature  in  two 
parallel  circuits,  and  if  we  allow  the  same  current 
density  in  the  armature  wires,  we  shall  obtain  a 
continuous  current  of  twice  the  strength  of  the 
alternating  current.  On  the  other  hand,  the  alter- 
nating current  will  have  2*22  times  the  voltage,  so 
that  the  output  of  the  alternator  will  be  1 1  per 
cent,  greater  than  that  of  the  continuous  current 
machine.  In  the  alternator  we  save  the  commuta- 
tor, and  you  see,  therefore,  that  for  equal  output 
the  alternator  is  a  cheaper  and  lighter  machine 
than  the  continuous  current  dynamo. 

The  alternator  shown  in  Fig.  14  is,  however,  not 
the  kind  of  machine  used  in  practice.  I  have  only 
chosen  it  as  a  simple  example  to  show  the  relation 
between  continuous  and  alternate  current  machines. 
In  practice  the  latter  are  made  with  a  number  of 
poles  in  order  to  bring  down  the  speed  to  reasona- 


ALTERNATING    CURRENT    MACHINES.  63 

ble  limits,  and  the  wire  is  not  bunched  together, 
but  is  spread  more  or  less  over  the  surface  of  the 
armature.  There  is  also  this  difference :  that  the 
poles  of  the  field  surround  the  armature  more 
closely,  and  consequently  the  transition  from  a 
north  to  a  south  field  is  more  abrupt,  than  in  Fig. 
14.  Notwithstanding  these  differences,  the  elec-, 
tromotive  force  of  alternators  as  practically  made 
is  very  nearly  that  given  in  Formula  (i  i),  and  the 
comparison  of  weight  and  cost  which  we  found 
just  now  holds  good  for  the  machines  as  actually 
built. 

You  will  see  from  the  diagram  on  the  wall  that 
alternators  are  all  characterized  by  two  main  fea- 
tures— a  corona  or  ring  of  magnet  poles  and  a  ring 
of  armature  coils,  either  one  or  the  other  being 
movable.  The  particular  shape  of  the  poles,  their 
arrangement  mechanically,  the  method  of  winding 
the  armature  coils,  and  many  other  details,  may  be 
changed  in  many  ways,  but  the  main  features  re- 
main the  same. 

For  purposes  of  study  it  is  convenient  to  imagine 
the  pole  ring  and  the  armature  ring  cut  open  and 
spread  into  straight  lines.  We  need  then  only 


64  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

consider  one  coil  and  two  or  three  poles,  as  shown 
in  Fig.  15.  The  electromotive  force  at  any  mo- 
ment is  obviously  proportional  to  the  number  of 
wires  which  happen  at  that  moment  to  be  covered 
by  one  or  both  poles,  care  being  taken  to  count,  in 


LnJ 


FIG.  15. 

the  latter  case,  the  difference  in  the  number  of 
wires,  since  the  poles  act  differentially.  We  can 
thus  plot  a  curve  giving  the  resultant  electromotive 
force  as  a  function  of  the  position  of  the  coil  in 
front  of  the  poles,  and  since  at  constant  speed  this 
position  changes  proportionately  with  the  time,  the 
curve  also  gives  us  the  electromotive  force  as  a 
function  of  the  time.  Now  you  will  easily  see  that 
the  shape  of  this  curve  depends  on  the  width  of 
the  poles  and  length  of  coil.  It  also  depends  on 
their  relative  shape.  But  not  to  complicate  our 
investigation  too  much,  I  assume  that  both  poles 
and  coils  are  rectangular,  which  in  machines  of  the 


ALTERNATING    CURRENT    MACHINES.  65 

Westinghouse  and  Lowrie  Hall  type  is  strictly,  and 
in  most  other  machines  is  approximately,  true.  As 
an  extreme  case  regarding  the  width  of  poles,  we 
may  take  a  machine  in  which  the  north  and  south 
poles  are  placed  so  close  as  almost  to  touch  each 
other.  In  this  case  the  width  of  poles  is  equal  to 
their  distance  or  pitch.  Machines  with  alternate 
poles  set  so  closely  are  not  made ;  but  the  Mordey, 
in  which  poles  of  the  same  sign,  separated  by  equal 
intervals  of  blank  or  neutral  spaces,  is  a  practical 
illustration  of  the  same  principle.  Suppose  now 
that  we  put  into  such  a  field  an  armature,  the  whole 
surface  of  which  is  covered  by  coils,  then  the  length 
of  each  coil  must  also  equal  the  pitch,  and  there 
will  then  be  only  one  position,  namely,  that  in 
which  the  centre  of  the  coil  coincides  with  the 
centre  of  the  pole,  when  all  the  wires  in  the  coil 
are  producing  electromotive  force  in  the  same  di- 
rection. In  every  other  position  the  electromotive 
force  in  one  part  of  the  coil  is  opposed  to  that  in 
the  other  part.  In  such  a  machine  the  wire  is  not 
used  to  the  greatest  advantage,  and  the  electromo- 
tive force  curve  becomes  a  zigzag  line  as  shown  in 
Fig.  1 6.  The  question  which  interests  us  most  is 
5 


66  ALTERNATING   CURRENTS  OP  ELECTRICITY. 

that  of  the  effective  electromotive  force  represented 
by  this  curve.  Experimentally  we  can,  of  course, 
easily  determine  it.  We  need  only  connect  a  Car- 
dew  voltmeter  to  the  terminals  of  the  coil  and  take 
a  reading ;  but  it  is  important  to  know  beforehand, 
that  is,  before  the  machine  is  built,  what  volts  we 
may  expect  to  get.  Consider  for  a  moment  what 
it  really  is  that  the  voltmeter  measures.  It  is  the 


NORTH 

SOUTH  OR   ) 
NEUTRAL 

NORTH 

1 

IHttlllllli 

ARMATURE 

X 

FIG.   16. 

amount  of  heat  developed  per  second  in  its  wire. 
With  the  quick  alternations  produced  by  the  ma- 
chine there  is  no  time  for  the  wire  to  change  its 
temperature,  and  its  resistance  is  therefore  con- 
stant. The  amount  of  heat  dissipated  per  second 
is  then  the  square  of  the  effective  volts  divided  by 
the  resistance,  and  this  is  also  equal  to  the  integral 
of  the  square  of  the  instantaneous  volts  multiplied 


ALTERNATING    CURRENT    MACHINES.  67 

by  the  differential  of  the  time,  the  integration 
being  extended  over  one  second;  or  we  may  ex- 
tend the  integration  only  over  the  time  occupied 
by  one  half  period  and  divide  the  result  by  that 
time;  this  will  also  give  us  the  heat  per  second. 
But  as  we  want  to  know  the  volts  and  not  the  heat 
generated  per  second,  we  need  not  concern  our- 
selves about  the  resistance  of  the  voltmeter  wire  at 
all,  and  simply  take  the  square  root  of  the  integral 
£dt;  this  gives  the  effective  volts.  To  do  this 
graphically,  as  shown  in  Fig.  16,  scale  theordinates 
of  the  zigzag  line,  square  the  readings,  and  plot  to 
an  arbitrary  scale  the  result.  Thus  we  obtain  the 
tent-like  figure  shown  in  the  diagram,  the  area  of 
which  is  the  integral,  or,  to  speak  quite  correctly, 
is  proportional  to  the  integral  of  square  of  instan- 
taneous volts  and  time.  The  height  of  a  rectangle, 
of  equal  base  and  area,  is  the  square  of  the  effective 
volts.  It  is  thus  possible  to  determine  beforehand, 
for  any  given  arrangement  of  field  poles  and  arma- 
ture coils,  what  the  effective  volts  will  be,  and, 
roughly  speaking,  the  larger  the  shaded  area,  the 
higher  will  be  the  voltage  of  the  machine.  For 
instance,  in  Fig.  17,  I  have  assumed  that  the  field 


68 


ALTERNATING   CURRENTS   OF   ELECTRICITY. 


of  Fig.  1 6  has  been  retained,  but  that  the  armature 
coils  have  been  made  only  half  the  length  for  the 
same  number  of  turns.  Only  half  the  surface  of 


\ 


FIG.  17. 


the  armature  is  now  covered  by  wire,  and  the  max- 
imum electromotive  force  is  maintained  for  a  quar- 
ter period  instead  of  being  momentary  as  before. 
This  gives  a  trapezoidal  line  for  the  electromotive 
force  curve,  and  the  shaded  area  is  now  considera- 


FIG.  18. 


\ 


bly  larger  than  before.  Let  us  now  go  back  to  the 
first  armature,  and  run  it  in  a  field  the  poles  of 
which  are  only  half  the  width,  the  total  induction 
being,  however,  the  same.  Here  again  we  get  a 


ALTERNATING    CURRENT    MACHINES.  69 

trapezoidal  electromotive  force  curve  (Fig.  18),  and 
the  same  voltage  as  in  Fig.  17.  If  we  now  shorten 
the  coils,  we  come  back  to  the  zigzag  lines,  but  the 
peaks  are  higher  (Fig.  19),  and  the  voltage,  as 
shown  by  the  shaded  area,  is  again  increased.  The 
arrangement  shown  in  Fig.  19  is  that  usually  met 
with  in  modern  alternators,  but  owing  to  the  fringe 
of  lines  at  the  corners  of  the  pole  pieces,  the  elec- 


\ 


FIG.  19. 


tromotive  force  curve  is  not  quite  as  sharp  as  here 
shown.  The  peak  is  rounded  off  and  the  sides  are 
more  wavy,  the  curve  approaching,  in  fact,  very 
nearly  to  a  true  sine  curve.  Leaving,  however, 
such  refinements  aside,  it  is  easy  to  work  out  an 
expression  for  the  effective  volts  in  each  given 
case  either  graphically  by  the  use  of  such  diagrams 
as  Figs.  1  6  to  19,  or  analytically.  The  operation 


7<D  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

is  somewhat  laborious,  but  in  no  sense  difficult, 
and  it  would  be  useless  to  burden  this  lecture  with 
it.  I  will  merely  state  the  results.  If  you  will 
refer  back  to  Formula  ( 1 1 )  you  will  see  that  the 
effective  electromotive  force  of  a  simple  coil,  re- 
volving in  a  uniform  field,  is  given  by  the  product 
of  a  constant  (in  this  case  2*22),  the  total  induction 
or  number  of  lines  emanating  from  one  field  pole, 
the  number  of  wires  counted  on  both  sides  of  the 
coil,  and  the  frequency.  If,  instead  of  a  machine 
with  two  poles  and  one  coil,  we  had  made  a  ma- 
chine with  10  poles  and  five  coils,  coupled  in  series, 
the  electromotive  force  of  each  coil  w.ould  have 
been  five  times  as  great;  if  the  machine  at  20  poles 
and  10  coils  it  would  have  been  10  times  as  great, 
and  so  on.  You  see,  therefore,  that  the  electro- 
motive force  is  simply  proportional  to  the  total 
number  of  wires  coupled  in  series,  and  to  the  num- 
ber of  pairs  of  poles,  and  Formula  (i  i)  is  right  for 
a  machine  with  any  number  of  poles.  The  same 
kind  of  formula  is  also  correct  for  any  arrangement 
of  poles  and  coils,  but  the  coefficient  is  different  in 
each  case.  This  coefficient  is  really  the  ratio  of 
the  electromotive  force  of  the  alternator  to  that  of 


ALTERNATING    CURRENT    MACHINES.  7  1 

a  continuous  current  dynamo  of  equal  weight  and 
arrangement  of  field  and  armature.  If  the  machine 
has  r  pairs  of  poles,  and  runs  at  a  speed  of  N  revo- 
lutions per  minute,  its  electromotive  force  of  a  con- 
tinuous current  machine  is 


(12), 


or  if  by  Z  we   denote  field  strength  in   English 
measure  — 


e  =  /ZrNio-°       .................  (13). 

Let  K  be  the  coefficient  which  depends  on  the 
shape  of  poles  and  armature  coils,  then  the  elec- 
tromotive force  of  our  alternator  is 

N 
e  =  K/Fr—  io~8       ................  (14). 


.............  .....(15). 

e  =KFr«io-8      ...................  (16). 

To  find  the  electromotive  force  we  must  therefore 
determine  the  coefficient  K  for  each  case,  and,  as 
I  have  already  said,  this  is  not  a  difficult  mathe- 
matical problem.  The  result  for  the  cases  I  have 
brought  before  you  is  as  follows  :•  — 


72  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

(i).  If  machine  gives  a  strictly  sinu- 
soidal electromotive  force,         .  ^=2-22 
(2).  Width  of  poles  equal  to  pitch,  and 

length  of  coils  equal  to  pitch,    .      =  1*160 
(3).   Width  of  poles  equal  to  pitch,  and 
length  of  coils  equal  to  half  the 
pitch,         ;;       ."      r;         .        a_  .   =1-635 
(4).  Width  of  poles  equal  to  half  the 
pitch,  and  length  of  coils  equal 
to  pitch,    .          .          .          .  =  1-635 

(5).  Width  of  poles  equal  to  half  the 
pitch,  and  length  of  coils  equal 
to  half  the  pitch,        .         .         .      =2-300 
If  you  compare  the    first  and  last  line  of  this 
table,  you  will  find  that  there  is  only  3*^  per  cent, 
difference  between  the  two  coefficients.     The  last 
line  refers  to  machines  as  actually  built,  and  the 
first  line  to  ideal  machines  having  a  true  sinusoidal 
electromotive  force  curve.     You  see  that,  as  far  as 
the  effective  electromotive  force  is  concerned,  the 
assumption   that  ordinary  commercial   alternators 
follow  the  sine  law  is  practically  correct. 


CHAPTER  V. 

• 

MECHANICAL   CONSTRUCTION   OF   ALTERNATORS. 

Speaking  generally,  we  may  say  that  the  con- 
structive requirements  and  the  points  to  which  par- 
ticular attention  must  be  paid  in  designing  alterna- 
tors are  very  much  the  same  as  obtain  in  dynamos, 
but  there  may  be  certain  differences.  In  the  first 
place,  the  armature  of  a  dynamo  is,  on  account  of 
its  commutator  and  brushes,  necessarily  more  com- 
plicated than  that  of  an  alternator.  On  the  other 
hand,  the  field  is  simpler.  The  majority  of  dyna- 
mos are  made  for  low  or  moderate  voltage,  whilst 
alternators  are  generally  made  for  high  voltage. 
This  requires  greater  care  in  the  insulation,  and 
compels  us  to  avoid  certain  methods  of  winding, 
which  for  a  loo-volt  dynamo  are  quite  admissible. 
In  the  design  of  both  kinds  of  machine  we  must 
pay  attention  to  eddy  currents  and  hysteresis,  but 
in  alternators  these  disturbing  and  injurious  effects 

73 


74  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

are  far  more  serious  than  in  dynamos.  The  reason 
is  that  both  the  wire  and  the  iron,  if  the  armature 
has  an  iron  core,  are  subjected  to  a  more  rapid 
reversal  of  induction.  Special  precautions  must 
therefore  be  adopted.  The  core  must  be  well  lam- 
inated, and  the  conductor  should  not  exceed  a  cer- 
tain section.  What  that  maximum  section  should 
be  depends,  of  course,  on  the  general  design  of  the 
alternator,  but  we  may  take  it  roughly  that,  where 
round  wire  is  used,  its  diameter  should  not  exceed 
140  mils.,  and  where  strip  is  used  its  thickness 
should  not  be  more  than  100  mils.  Another  and 
very  effectual  cure  for  eddy  currents  is  to  embed 
the  conductor  entirely  in  iron,  an  arrangement 
which  has  been  first  proposed  by  Wenstrom,  and 
has  been  largely  used  by  Brown,  the  latest  example 
being  his  large  three-phase  current  alternator  at 
Lauffen.  The  conductor  is  a  solid  copper  rod  of 
about  1^2  inches  in  diameter,  threaded  through 
holes  in  the  armature  core.  A  conductor  of  that 
size,  if  placed  on  the  surface  of  an  armature  where 
it  is  subjected  to  some  80  field  reversals  per  second, 
would  get  hot  in  a  few  minutes,  yet,  arranged  as  it 
is  in  Mr.  Brown's  "  three-phaser, "  it  keeps  perfectly 


MECHANICAL    CONSTRUCTION    OF    ALTERNATORS.         75 

cool.  It  is  the  fact  that  the  conductor  is  sur- 
rounded on  all  sides  by  iron  which  produces  this 
result.  A  still  more  striking  illustration  of  the 
effect  of  iron  in  preventing  eddy  currents  is  Thom- 
son's welding  machine.  Here  we  have  a  solid 
conductor  of  many  square  inches  in  area,  in  which 
the  welding  current  is  generated.  But  this  con- 
ductor is  the  secondary  circuit  of  a  transformer, 
and  is  surrounded  by  the  iron  of  the  transformer. 
Professor  Thomson's  explanation  of  the  fact  that 
in  all  such  cases  eddy  currents  are  avoided  is  that 
the  speed  at  which  the  wire  cuts  through  the  lines 
of  force  is  much  greater  than  its  speed  of  motion, 
that,  in  fact,  the  lines  at  first  yield  and,  so  to  say, 
stretch,  but  finally,  when  the  tension  becomes  too 
great,  snap  suddenly  past  the  wire.  Thus  all  parts 
of  the  wire  are  cut  at  almost  the  same  instant  by 
the  lines  of  force,  and  this  leaves  no  time  during 
which  the  differences  of  electromotive  force,  and, 
therefore,  eddy  currents,  could  be  developed  in  the 
wire.  I,  personally,  do  not  feel  competent  to  either 
confirm  or  refute  this  explanation,  but  coming  from 
so  high  an  authority  as  Professor  Elihu  Thomson, 
am  satisfied  to  accept  it.  That  wires  embedded  in 


76  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

iron,  or  surrounded  on  all  sides  by  iron,  are  nearly 
free  from  eddy  currents  is,  however,  an  undoubted 
fact. 

From  what  I  have  here  said  you  will  see  that  in 
one  way  or  another  we  can  avoid,  or  at  least  greatly 
reduce,  the  loss  of  power  by  eddy  currents  in  alter- 
nators. Now  let  us  see  whether  this  is  also  the 
case  with  the  other  source  of  loss,  namely,  "  hyste- 
resis. "  Under  this  term  we  comprise  a  certain  phe- 
nomenon, first  investigated  by  Ewing,  and  which 
maybe  popularly  described  as  "magnetic  friction." 
The  lines  of  force  in  being  forcibly  dragged  through 
the  iron  core  of  the  armature  continually  change 
its  magnetization,  and  the  core,  even  if  most  care- 
fully laminated,  so  as  to  avoid  eddy  currents,  still 
becomes  hot  if  revolved  in  an  excited  field.  It  is 
at  once  obvious  that  the  power  thus  wasted  will  be 
the  greater  the  more  rapid  the  reversal  of  magneti- 
zation, and  the  greater  its  amount.  This  loss  takes 
place  in  dynamos  as  well  as  in  alternators,  but  to  a 
different  extent.  In  a  dynamo  the  reversal  is  com- 
paratively slow.  Take,  for  instance,  a  two-pole 
machine,  running  at  600  revolutions  per  minute,  or 
10  revolutions  per  second.  The  whole  mass  of  the 


MECHANICAL   CONSTRUCTION    OF    ALTERNATORS.         77 


armature  core  undergoes,  therefore,  in  every  second 
ten  complete  cycles  of  magnetic  change.  But  in 
modern  alternators  the  change  is  about  ten  times 
as  rapid,  the  frequency  being  100.  If  we  allowed 
the  same  induction,  that  is,  number  of  lines  per 
square  centimetre  of  core  section,  the  alternator 
would  waste  ten  times  the  power,  and  this  would, 
of  course,  be  inadmissible.  There  is  only  one 
way  in  which  we  can  reduce  the  waste  of  power, 
and  that  is  by  adopting  a  lower  induction.  Thus, 
whilst  in  dynamos  the  induction  ranges  from  14,000 
to  20,000  lines  per  square  centimetre,  it  is  only 


fc. 


8000   4000    6000    8000   10000   12000   14000   10000   18000   20000 
INDUCTION 

FIG.  20. 

about  5,000  in  alternators.     The  exact  induction  at 
which  it  is  best  to  work  varies,  of  course,  with  the 


78  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

type  and  size  of  machine,  and  as  every  design  is  a 
compromise,  you  must  not  consider  the  5,000  as  a 
hard-and-fast  rule.  To  enable  you,  however,  to 
deal  with  each  given  case  on  its  own  merits,  I  give 
in  Fig.  20  a  curve  showing  the  loss  of  power  by 
hysteresis  per  ton  of  iron  when  the  frequency  is 
100.  The  induction  is  measured  on  the  horizontal, 
and  the  power  (in  kilowatts)  on  the  vertical.  This 
curve  has  been  compiled  from  the  experimental 
results  of  Professor  Ewing.  I  may  incidentally 
mention  that  this  curve  is  approximately  repre- 
sented by  the  equation — * 

(B  \l's>s> 
1        .(17), 
1 0007 

or  if  the  induction  B  is  given  in  English  lines  per 
square  inch — 

Power  =  -160  B1-65 (18). 

The  power  is  given  in  kilowatts  per  ton  of  iron 
when  the  frequency  is  100  complete  cycles  per  sec- 
ond. For  a  different  frequency  the  power  is  pro- 
portionally altered. 

*  Steinmetz  in  his  classical  researches  on  hysteresis  gives  the 
exponent  as  1.6. 


MECHANICAL  CONSTRUCTION  OF  ALTERNATORS.    79 

There  being  necessarily  always  some  waste  of 
power,  if  the  armature  has  an  iron  core  it  was  nat- 
ural that  inventors  should  turn  their  attention  to 
the  construction  of  an  alternator  with  a  coreless 
armature.  In  fact,  the  Meritens  machine,  which 
was  one  of  the  first  commercial  alternators,  and  is 
used  to  this  day  in  lighthouse  work,  has  no  iron  in 
the  armature.  Then  there  comes  the  Siemens,  also 
without  iron,  the  Ferranti,  and  the  Mordey.  In  all 
these  machines  the  loss  by  hysteresis  is  avoided, 
and  if  this  were  the  only  consideration,  they  would 
undoubtedly  be  better  than  their  rivals  with  iron- 
cored  armatures.  But  as  I  have  said  before,  every 
design  is  a  compromise,  and  it  is  quite  possible 
that  the  machine  with  iron  in  its  armature  is  as 
good  a  compromise  as  one  without  iron.  The  fact 
that  the  majority  of  American  machines,  all  the 
German  machines,  including  those  now  made  by 
Messrs.  Siemens  and  Halske,  and  a  good  half  of 
the  English  machines  have  iron-cored  armatures, 
is  in  itself  sufficient  proof  that  the  hysteresis  loss 
is  not  an  insurmountable  obstacle.  There  are  es- 
pecially two  points  in  favour  of  using  iron.  The 
first  is  that  we  are  thereby  enabled  to  give  the 


8o  ALTERNATING    CURRENTS   OF   ELECTRICITY. 

armature  greater  mechanical  strength  than  can  be 
done  in  machines  where  the  armature  coils  are  at- 
tached singly  and  held  by  insulating  material.  The 
second  is  that  the  presence  of  iron  tends  to  dimin- 
ish the  magnetic  resistance  of  the  air-gap,  and  thus 
saves  exciting  energy.  In  Mr.  Brown's  three- 
phaser,  for  instance,  the  total  exciting  energy  does 
not  amount  to  more  than  y2  per  cent,  of  the  total 
power. 

I  have,  a  moment  ago,  spoken  of  the  differences 
between  alternators  and  dynamos  from  an  electrical 
and  mechanical  point  of  view.  There  remains  yet 
to  notice  an  important  point  of  difference,  namely, 
the  absence  in  alternators  of  a  commutator  and 
brushes.  You  all  know  that  these  are  the  most 
delicate  parts  of  a  dynamo,  and  although  in  modern 
machines  of  moderate  voltage  these  parts  are  per- 
fectly reliable  and  easily  handled,  the  case  is  dif- 
ferent when  we  attempt  to  build  dynamos  for  1,000 
or  2,000  or  more  volts.  We  encounter  then  diffi- 
culties which  are  absent  from  alternators,  and  it  is 
mainly  on  this  account  that  engineers  who  have  to 
design  power  transmission  schemes  over  long  dis- 
tances are  beginning  to  turn  their  attention  to  some 


MECHANICAL    CONSTRUCTION    OF    ALTERNATORS.         8 1 

forms  of  alternator  as  the  most  certain  means  of 
solving  such  problems.  I  shall  have  something 
more  to  say  on  this  subject  in  the  third  lecture. 
For  the  present  I  must  limit  my  remarks  to  the 
machines  as  required  for  lighting. 
6 


CHAPTER   VI. 


DESCRIPTION   OF   SOME   ALTERNATORS. 

In  the  limited  time  at  my  disposal  it  would  be 
impossible  for  me  to  give  you  anything  like  an 
exhaustive  account  of  the  various  machines  now  in 
use.  I  shall  therefore  only  describe  a  few  of  them 
as  being  representative  examples. 

i.  The  Ferranti  Alternator. — The  field  magnets 
are  wrought-iron  bars  of  trapezoidal  section  (Fig. 


FERRANTI. 


FlG.    21. 


21),  cast  into  massive  yoke  rings,  which  can  be 
drawn  apart  at  right  angles  to  the  shaft,  so  as  to 
expose  the  armature  for  examination  and  repair. 


82 


DESCRIPTION   OP   SOME   ALTERNATORS.  83 

The  latter  is  of  disc  pattern,  and  the  coils  are  in- 
serted in  pairs.  The  conductor  is  a  corrugated 
copper  strip  wound  with  a  strip  of  vulcanized  fibre 
of  equal  width  upon  a  laminated  brass  core.  The 
conductor  is  thus  insulated  from  the  core,  and  the 
latter  is  insulated  from  the  supporting"  ring.  This 
double  insulation  is  an  important  feature  of  the 
machine.  The  core  is  held  in  gun-metal  cheeks, 
which  are  provided  with  side  wings  for  ventilation. 
The  attachment  of  each  pair  of  cheeks  to  the  sup- 
porting ring  is  by  means  of  a  shank  passing  through 
insulating  washers  into  a  cavity  in  the  ring,  and 
secured  by  a  nut.  The  cavity  is  cast  out  with  sul- 
phur. To  avoid  too  great  a  loss  by  eddy  currents 
the  conductor  is  made  very  thin;  the  winding  is 
split  up  into  two,  four,  or  more  parallel  circuits.  I 
may  here  incidentally  mention  that  where  an  arma- 
ture winding  is  thus  split  up,  great  care  must  be 
taken  to  have  all  the  magnets  of  equal  strength,  as 
otherwise  there  would  be  created  with  the  arma- 
ture differential  currents,  which  would  waste  far 
more  power  than  the  eddy  currents,  which  the  ar- 
rangement was  intended  to  avoid.  The  Ferranti 
machines  now  working  at  Deptford  are  giving  an 


84 


ALTERNATING    CURRENTS   OF   ELECTRICITY. 


electromotive  force  of  10,000  volts,  and  to  prevent 
flashing  over  to  the  magnets  the  latter  are  provided 
with  double  caps  of  ebonite. 

2.  The  Mordey  Alternator. — This  is  also  a  coreless 
machine  of  the  disc  pattern,  but  the  armature  is 
fixed  whilst  the  magnets  revolve.  The  armature 
coils  (Fig.  22)  are  wedge-shaped,  and  the  conductor 


1 


FIG.  22. 

is  a  thin  copper  strip  wound  on  a  slate  core,  the 
layers  being  separated,  as  in  the  Ferranti  coils,  by 
a  thin  strip  of  insulating  material.  The  attach- 
ment is  made  at  the  outer  and  wider  end  of  the  coil 
to  a  gun-metal  supporting  ring.  The  magnets  are 
of  cast-iron,  and  so  shaped  as  to  require  only  one 
coil  C  of  exciting  wire.  This  is  wound  on  a  cen- 


DESCRIPTION    OF    SOME    ALTERNATORS.  85 

tral  cylindrical  partjj/,  to  both  sides  of  which  are 
pole  pieces  of  peculiar  star-like  form.  Thus 
the  poles  on  one  side  of  the  armature  are  all  of  the 
same  sign,  and  those  on  the  other  side  are  of  the 
opposite  sign,  the  lines  of  force  passing  from  N  to 
S  at  right  angles  through  the  surface  of  the  arma- 
ture, and  all  in  the  same  direction.  There  is  thus, 
properly  speaking,  no  reversal  of  magnetization, 
but  merely  a  change  from  full  induction  when  a 
wire  is  between  opposite  poles,  to  no  induction 
when  it  is  between  neighbouring  poles,  and  the 
general  effect  is  the  same  as  if  we  had  half  the  field 
strength  alternating.  To  apply  our  formulae  for 
the  electromotive  force  of  this  machine  we  must, 
therefore,  introduce  not  the  whole  field  strength  F 
or  Z,  but  half  its  real  value. 

3.  The  Westinghouse  Alternator. — As  a  good  ex- 
ample of  an  alternator,  the  armature  of  which  con- 
tains iron,  we  may  take  the  Westinghouse  machine, 
which,  in  its  important  details,  is  very  .similar  to 
the  Thomson-Houston.  The  armature  is  cylindri- 
cal (Fig.  23),  and  is  covered  by  link-shaped  coils, 
with  the  wires  parallel  to  the  shaft,  the  rounded 
ends  of  the  coils  C  being  bent  inwards,  and  secured 


86  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

to   the  end  faces   of  the   armature    core.     In    the 
Thorn  son- Houston  machines  the  coil  ends  are  not 


turned  inwards.  The  field  magnets  NS  are  set 
radially  outside  the  armature,  and  their  outer  ends 
are  connected  by  a  yoke  ring  Y.  According  to  our 
theory,  the  best  arrangement  as  regards  width  of. 
coil  is  half  the  pitch,  which  means  that  the  central 
space  of  the  coil  should  have  the  same  width  as  the 
magnet,  but  Professor  Thomson,  when  experiment  ~ 
ing  with  various  coils,  found  that  a  coil  having  a 
slightly  smaller  internal  space  gave  a  higher  elec- 
tromotive force  when  the  machine  was  working 
under  full  load.  His  explanation  is  that  the  cur- 
rent in  the  armature  wires  alters  the  original  mag- 
netization of  the  field,  tending  to  concentrate  the 
lines  towards  the  leaving  edge  of  the  pole  piece, 
and  thus  produces  a  more  intense  but  narrower 


DESCRIPTION    OF    SOME    ALTERNATORS.  87 

field.  The  inner  space  of  the  coils,  which  is  free 
from  winding,  should  therefore  also  be  made  nar- 
rower. 

4.    The  Kapp  Alternator. — In  this  machine  (Fig. 
24)  the  armature  is  of  the  disc  pattern,  and  con- 


tains  an  iron  core  A  made  by  coiling  a  strip  of  thin 
charcoal-iron  with  a  strip  of  paper  upon  a  support- 
ing ring.  The  coils  are  wound  transversely  round 
the  core.  The  field  magnets  in  the  larger  ma- 
chines are  of  wrought  iron,  with  expanded  pole 
shoes,  and  are  set  parallel  to  the  shaft  on  both  sides 
of  the  armature  core,  presenting  the  same  poles 
NN  SS  on  opposite  sides.  The  outer  ends  of  the 
magnets  are  joined  by  cast-iron  yokes  YY.  Owing 
to  the  angular  position  of  the  pole  shoes,  each  wire 
does  not  enter  the  field  simultaneously  over  its 


88  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

whole  length,  but  the  entry  is  a  little  more  gradual, 
whereby  the  sharp  peaks  in  the  line  of  electromo- 
tive force  (Fig.  19)  are  toned  down,  and  the  curve 
is  made  to  approach  a  sinusoidal  form.  The  cur- 
rent is  collected  by  rubbing  contacts  from  insulated 
rings,  which  are  set  on  opposite  sides  of  the  arma- 
ture, that  is,  so  far  apart  that  it  is  impossible  for 
a  man  to  touch  both  simultaneously.  The  coeffi- 
cient K  for  this  machine  varies  between  2-3  and 
2  •/,  according  to  the  particular  design  chosen. 

5.  The  Kingdon  Alternator. — In  all  the  machines 
described  up  to  here,  the  wire,  either  on  the  field 
or  on  the  armature,  is  in  motion,  but  in  the  King- 
don machine  all  the  wires  are  at  rest,  the  only  re- 
volving part  being  an  armature  containing  no  wire. 
The  machine  consists  of  a  laminated  iron  cylinder, 
with  radial  teeth  projecting  inwards,  and  the  arma- 
ture and  field  coils  are  wound  over  alternate  teeth. 
The  revolving  part  is  a  wheel  provided  with  half 
as  many  laminated  iron  keepers  as  there  are  teeth 
in  the  stationary  part,  and  these  keepers  are  so 
arranged  as  to  bridge  magnetically  neighbouring 
teeth.  Thus  the-  teeth  over  which  the  armature 
coils  are  wound  become  alternately  parts  of  a  posi- 


DESCRIPTION    OF    SOME    ALTERNATORS. 


live  and  negative  magnetic  circuit,  and  an  alternat- 
ing current  is  produced. 

6.  The  Kennedy  Alternator. — Mr.  Kennedy  has 
further  developed  this  idea,  mainly  by  reducing  the 
number  of  armature  and  field  coils,  and  avoiding 
the  generation  of  an  alternating  current  in  the  lat- 


0 


FIG.  25. 

ter.  The  machine  (Fig.  25).  has  two  armature  and 
two  field  coils  wound  in  pairs,  and  placed  into  re- 
cesses in  a  skeleton  frame  of  soft  iron  laminated 
bars.  There  are  two  keeper  wheels  on  the  spindle, 
but  stepped  in  relation  to  each  other  by  half  a 
period,  so  that  when  the  keepers  of  one  wheel  have 


90  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

completely  closed  the  magnetic  circuits  around  one 
pair  of  field  and  armature  coils,  the  keepers  of  the 
other  wheel  are  midway  between  the  fixed  bars, 
and  the  magnetic  circuits  around  the  second  pair  of 
armature  and  field  coils  are  interrupted.  The  elec- 
tromotive force  in  those  coils  is  at  that  moment 
zero,  and  it  is  also  zero  in  the  other  coils,  through 
which  the  induction  is  a  maximum.  Half  a  period 
later  the  induction  becomes  a  maximum  in  the  sec- 
ond, and  zero  in  the  first  pair  of  coils,  and  this 
change  of  induction  produces  an  alternating  elec- 
tromotive force  in  all  the  coils.  Now  it  is  obvi- 
ously possible  to  couple  the  two  field  coils  in  series, 
and  in  such  way  that  the  electromotive  force 
created  in  one  is  opposed  to  that  in  the  other,  and 
thus  to  neutralize  the  reaction  of  the  keeper  on  the 
exciting  circuit.  The  exciting  dynamo  has  then 
merely  to  overcome  the  ohmic  resistance  of  the 
two  coils,  as  in  any  other  machine.  The  two  arma- 
ture coils  may  be  coupled  in  series  or  parallel. 


CHAPTER  VII. 

TRANSFORMERS. 

I  have  already  drawn  your  attention  to  the  fact 
that  alternators  are  generally  designed  for  high 
voltage.  The  reason  is  obvious.  If  we  wish  to 
carry  the  current,  be  it  for  lighting  or  power,  to 
any  distance,  we  must  use  a  high  voltage,  in  order 
to  bring  the  section  of  our  conducting  wires  or 
mains  down  to  a  size  which  makes  the  whole  enter- 
prise commercially  possible.  But  to  give  our  cus- 
tomers a  current  of  some  thousands  of  volts  would 
be  dangerous  and  inconvenient,  for  glow  lamps  re- 
quire a  current  of  about  100  volts  when  arranged 
in  parallel,  that  is,  in  the  way  in  which  they  are 
of  most  use  to  private  consumers.  The  question 
therefore  arises  what  to*  do  with  our  high-pressure 
current  when  we  have  brought  it  to  the  place  where 
its  energy  is  required  for  lighting  lamps.  Obvi- 
ously we  must  transform  it ;  we  must  lower  its  volt- 

91 


p2  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

age  and  increase  its  strength.  Now  there  are  two 
ways  in  which  this  may  be  done.  We  may  use 
the  current  to  work  a  motor,  and  use  the  power 
given  out  by  the  motor  to  drive  a  dynamo  of  100  or 
200  volts.  The  direct  current  can  then  be  distrib- 
uted to  the  lamps  in  the  usual  way,  and  we  may 
even  supplement  the  installation  by  secondary  bat- 
teries, so  as  to  be  able  to  shut  down  our  machinery 
during  the  hours  of  minimum  demand.  As  far  as 
I  know,  this  system  of  transformation  has  only,  up 
to  now,  been  used  in  one  installation,  namely,  at 
Cassel,  in  Germany.  At  the  first  glance  it  may 
seem  complicated  and  costly,  but  it  has  many  ad- 
vantages, which  will  probably  lead  to  its  adoption 
in  other  towns. 

The  other  system  which  is  at  present  in  general 
use  is  that  of  direct  transformation  by  means  of 
induction  coils.  Here  we  need  no  moving  machin- 
ery, but  simply  a  stationary  apparatus  consisting  of 
a  laminated  iron  core  and  two  coils  (Fig.  26).  One 
of  these  consists  of  many  turns  of  fine  wire,  and  is 
technically  termed  the  primary  coil  P,  and  the 
other  of  fewer  turns  of  stouter  wire  called  the 
secondary  coil  S.  The  high-pressure  current  is 


TRANSFORMERS. 


brought  by  the  mains  w,  and  the  low-pressure  cur- 
rent is  supplied  to  the  lamp  L  by  the  secondary 
mains  W.  You  will  observe  that  there  is  abso- 
lutely no  connection  between  the  two  sets  of  mains, 
and  this  is  a  great  guarantee  for  the  safety  of  the 
system.  The  action  of  this  apparatus,  which  is 
technically  known  under  the  name  of  "trans- 


w 


w 


\Vv\j 


w 


PIG.  26. 


former,"  will  be  clear  to  you  from  what  I  have  said 
in  the  first  lecture  about  the  generation  of  an  alter- 
nating electromotive  force.  The  primary  coil  mag- 
netizes the  iron  core  in  alternate  directions,  and  at 
each  reversal  the  lines  of  force  cut  through  the 
wires  of  the  secondary  coil.  The  latter  must  there- 
fore become  the  seat  of  an  alternating  electromotive 
force.  If  we  denote  by  F  the  total  induction,  and 


94  ALTERNATING   CURRENTS  OF   ELECTRICITY. 

call  n  the  frequency,  the  maximum  electromotive 
force  generated  in  each  turn  of  wire  is 


and  the  effective  electromotive  force  is  this  value 
divided  by  the  square  root  of  2.  If  the  coil  con- 
tains TU  turns,  the  total  effective  electromotive  force 
in  the  large  circuit  will  be 

e^  —  4-45  7/FTa  io"8  volts      ............  (19). 

The  changing  induction  affects,  however,  not 
only  the  secondary,  but  also  the  primary  coil,  and 
in  the  latter  there  will  be  developed  an  electromo- 
tive force  which  we  compute  by  the  same  formula, 
only  substituting  for  ra  the  number  of  primary 
turns  T,.  You  see,  therefore,  that  the  transforming 
ratio  is  given  by  the  ratio  of  the  turns  of  wire  in 
each  coil  ;  but  this  is  only  approximate,  since  not 
the  whole  electromotive  force  generated  in  the  sec- 
ondary reaches  its  terminals.  We  must  deduct  the 
electromotive  force  used  up  in  overcoming  the 
ohmic  resistance  of  the  secondary  coil.  In  like 
manner  the  electromotive  force  which  opposes  the 
current  in  the  primary  coil  is  a  little  smaller  than 
the  terminal  electromotive  force,  because  the  ohmic 


TRANSFORMERS.  $5 

resistance  also  opposes  the  primary  current.  The 
transforming  ratio  therefore  varies  with  the  load, 
but  I  may  at  once  say  that  in  good  transformers 
the  variation  as  determined  by  ohmic  resistance  is 
exceedingly  small,  generally  about  2  per  cent. 
There  is,  however,  another  cause  of  variation, 
namely,  magnetic  leakage,  and  a  transformer  made 
as  shown  in  Fig.  26  would  exhibit  this  phenom- 
enon in  a  most  objectionable  degree.  You  see  that 
the  two  coils  meet  in  the  middle  of  the  core.  Now 
the  primary  wants  to  magnetize  the  core  in  one 
direction  and  the  secondary  wants  to  magnetize  it 
in  the  opposite  direction.  The  result  is  that  the 
two  streams  of  induction  come,  so  to  speak,  into 
collision  about  the  middle  of  the  core,  and  some  of 
the  lines  which  the  primary  coil  tries  to  shoot 
through  the  secondary  are  squeezed  out  sidewise, 
and  contribute  nothing  to  the  secondary  electro- 
motive force.  You  might  perhaps  think  that  this 
is  of  no  moment,  for  we  can  make  up  for  the  loss 
of  these  lines  by  putting  a  few  more  turns  of  wire 
on  the  secondary.  But  if  we  did  that  we  should 
get  too  much  electromotive  force  at  light  loads. 
To  see  this  clearly  let  us  begin  with  no  load  on  the 


g  ALTERNATING    CURRENTS   OP   ELECTRICITY. 

secondary.  Then  there  is  no  current  in  S  and  no 
collision.  The  lines  created  by  the  primary  pass 
without  opposition  through  the  secondary,  and  F  in 
Formula  (19)  has  its  full  value.  Now  switch  on 
some  lamps  and  a  secondary  current  will  flow.  We 
shall  have  some  collision  of  lines,  and  F  in  the  for- 
mula, and  therefore  the  electromotive  force,  will 
become  smaller.  The  more  lamps  you  switch  on, 
the  more  current  flows  through  both  coils,  and  the 
more  violent  becomes  the  collision,  and  therefore 
the  number  of  lines  lost.  In  a  word,  we  generate 
more  lines  than  we  can  utilize.  The  obvious  rem- 
edy for  this  defect  is  to  place  the  coils  relatively  to 
each  other  into  such  a  position  that  the  lines  gen- 
erated by  the  primary  cannot  evade  passing  through 
the  secondary.  For  instance,  we  can  wind  one  coil 
over  the  other,  or  we  can  split  up  the  coils  into 
short  sections  and  place  them  alternately  over  the 
core.  Even  with  these  precautions  there  is  some 
magnetic  leakage,  but  this  does  not  as  a  rule  lower 
the  voltage  by  more  than  i  or  2  per  cent.  Thus  in 
a  good  transformer  we  may  expect  to  get,  with  con- 
stant primary  voltage,  a  terminal  pressure  varying 
between  102  and  99  or  98  volts,  when  the  load  is 


TRANSFORMERS.  97 

increased  from  zero  to  full  out-put.  These  figures 
refer  to  small  transformers  of  50  or  100  lamps. 
With  large  transformers  it  is  quite  possible  to  limit 
the  total  voltage  drop  to  something  under  2  per 
cent.  The  transformer  shown  in  Fig.  26  is  defec- 
tive in  other  ways  besides  its  great  voltage  drop. 
The  lines  passing  through  the  core  have  to  come 
back  through  air,  and  the  great  magnetic  resistance 
of  their  path  through  air  requires  a  strong  magne- 
tizing current,  or,  in  other  words,  the  primary  cur- 
rent will  be  considerably  greater  than  in  a  trans- 
former, in  which  the  return  path  is  made  more 
easy.  One  way  of  doing  this  is  to  increase  the 
surface  of  the  core  ends,  and  this  Mr.  Swinburne 
has  done  in  his  "  Hedgehog "  transformer.  The 
core  consists  of  iron  wires  which  at  the  ends  are 
curved  outwards.  Thus  part  of  the  return  path  is 
through  iron.  Another  method,  and  this  is  gen- 
erally used,  is  to  make  the  whole  return  path  of 
iron.  We  may,  for  instance,  employ  a  closed  iron 
frame  (J,  Fig.  27),  and  wind  the  primary  and  sec- 
ondary coils  C  over  each  other  on  two  opposite  sides 
of  this  frame.  The  iron  frame  or  core  is  composed 
of  thin  plates,  more  or  less  insulated  from  each 
7 


98 


ALTERNATING    CURRENTS   OF    ELECTRICITY. 


other  to  avoid  eddy  currents.  This  type  of  trans- 
former is  called  a  "core  transformer."  Or  we  may 
employ  only  one  coil  and  surround  it  by  a  double 


FIG.  27. 

frame,  as  in  Fig.  28,  a  kind  of  iron  shell,  and  this 
construction  is  called  a  "shell  transformer."  Both 
figures  have  been  drawn  to  represent  transformers 
of  equal  out-put.  The  depth  of  the  core  is  sup- 
posed to  be  equal,  and  its  width  in  Fig.  28  is  twice 
as  great  as  in  Fig.  27,  to  make  up  for  their  being 
only  one  coil.  At  the  first  glance  it  is  difficult  to 
say  which  is  the  better  transformer,  though  prac- 
tically the  balance  of  advantages  seems  to  lie  with, 
the  shell  type,  which  is  most  in  favour  with  the 
makers  of  this  kind  of  apparatus.  If  we  enquire 
what  it  is  we  must  aim  at  in  the  design  of  a  good 


TRANSFORMERS. 


99 


transformer,  we  find  that  the  length  of  wire  should 
be  small  in  order  to  reduce  ohmic  resistance  and 
cost,  that  there  should  be  as  little  iron  as  possible, 
and  that  the  magnetic  circuit  should  be  short.  Now 
these  are  contradictory  conditions.  To  reduce  the 
length  of  wire  we  must  work  with  a  high  total  in- 
duction, so  that  a  small  number  of  turns  should 
give  us  the  required  electromotive  force.  But  a 
large  induction  means  either  a  great  loss  by  hys- 
teresis or  a  stout  core,  and  a  stout  core  means  that 
the  length  of  each  turn  of  wire  is  great.  It  further 
means  a  longer  magnetic  circuit  and  a  greater 


FIG.  28. 


weight  of  iron,  which  again  increases  the  loss  by 
hysteresis.  You  see  here  again  the  successful  de- 
sign must  be  a  compromise,  but  a  compromise  in 


100  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

which  a  preponderance  of  weight  is  given  to  hys- 
teresis. We  must  remember  that  a  transformer  is 
continuously  at  work  whether  we  take  current  from 
it  or  not,  and  hence  the  hysteresis  loss  goes  on  day 
and  night.  Even  an  extra  loss  of  y2  per  cent,  by 
hysteresis  will  therefore  be  felt  in  the  all-day  effi- 
ciency of  the  apparatus,  and  is,  therefore,  more 
serious  from  an  economical  point  of  view  than  a 
loss  of  several  per  cent,  by  copper  resistance,  be- 
cause transformers,  when  used  for  lighting,  only 
work  a  very  short  time  daily  under  full  load.  On 
the  other  hand,  we  must  not  allow  an  excessive 
copper  loss,  as  this  would  disqualify  the  transformer 
on  account  of  too  great  a  voltage  drop.  We  are 
thus  hemmed  in  on  all  sides  by  conflicting  condi- 
tions, and  the  design  of  a  good  transformer  is  by 
no  means  so  easy  a  task  as  might  appear  at  the  first 
glance.  As  a  starting  point,  we  may  take  it  that 
the  magnetic  and  the  electric  circuit  should  be  as 
short  as  possible,  and  this  condition  will  be  best 
fulfilled  by  a  circular  or  square  shape,  or  as  near 
an  approach  to  such  a  shape  as  possible.  In  fact, 
if  you  examine  the  successful  transformers  in  the 
market,  you  will  find  that  this  condition  is  fulfilled 


TRANSFORMERS.  IOI 

in  either  one  or  the  other  circuit,  but  not  in  both. 
I  have  not  succeeded  in  estabHs-hi^g;  ^nd  I  "can 
therefore  not  give  you  any,  h^fd-and-fasfc  rules j  for 
the  construction  of  transformers,  b\lt 'hi  "ordei*  ^a 
enable  you  to  see  what  enormous  influence  slight 
alterations  in  the  proportions  have  on  the  weight 
and  cost  of  the  apparatus,  I  have  prepared  for  your 
proceedings  some  27  different  designs,  all  for  a 
loo-light  transformer.  Four  of  these  designs  are 
given  full  size  in  Plates  I.  and  II.,  pages  156-7. 
In  all  these  the  copper  loss  is  2  per  cent.  The 
hysteresis  loss  is  given  in  each  case.  You  can  see 
at  a  glance  what  a  great  difference  there  is  in  the 
amount  of  copper  required,  and  how  by  a  skilful 
choice  of  the  proportions  the  cost  of  the  apparatus 
can  be  reduced  without  lowering  its  efficiency. 

Before  concluding  this  part  of  my  subject,  I  wish 
to  draw  your  attention  to  the  relation  existing  be- 
tween the  linear  dimensions  of  a  transformer  and 
its  out-put  and  hysteresis  loss.  Imagine  that  after 
designing  a  score  or  so  of  transformers  you  have  at 
last  arrived  at  a  type  with  which  you  feel  satisfied ; 
but  suppose  it  is  not  the  size  you  want.  How  will 
you  alter  its  linear  dimensions?  Let  us  try  what 


102  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

we  shall  get  if  we  make  everything  twice  as  big, 
'  including;  tti^' size  of  the  wire.  We  retain  the  in- 
di;et.ion  per  square  "centimetre  at  the  4,000  or  5,000, 
kwliich'we  found"  will  give  us  a  loss  of  say  \y2  per 
cent,  by  hysteresis.  We  also  retain  the  number  of 
turns  in  both  coils.  The  total  induction  is  then 
four  times  as  great,  and  the  electromotive  force 
also  four  times  as  great.  The  resistance  of  the 
coils  has  been  reduced  to  one-half  its  former  value 
(area  of  wire  four  times  as  great,  and  length  twice 
as  great).  If  we  are  satisfied  to  have  the  same 
copper  loss,  we  can  allow  a  current  which  will  give 
us  four  times  the  previous  voltage  loss,  but  as  the 
resistance  has  been  halved  the  current  will  be  eight 
times  its  former  value.  Thus  the  current  is  eight 
times  and  the  volts  are  four  times  as  great  as  be- 
fore; the  out-put  will,  therefore,  be  32  times  as 
great.  But  32  is  two  to  the  fifth  power,  and  hence 
we  see  that  the  out-put  of  a  transformer  varies 
as  the  fifth  power  of  its  linear  dimensions.  The 
weight,  cost,  and  hysteresis  loss,  on  the  other  hand, 
all  vary  as  the  cube  of  the  linear  dimensions,  and 
the  weight  per  kilowatt  of  out-put  varies  inversely 
as  the  square  of  the  linear  dimensions.  Or,  in  fig- 


TRANSFORMERS.  103 

ures,  if  40  Ibs.  of  copper  and  iron  were  required  for 
each  kilowatt  produced  by  the  small  transformer, 
only  10  Ibs.  per  kilowatt  will  be  required  in  the 
larger ;  and  if  the  small  transformer  wasted  2  per 
cent,  of  its  power  in  hysteresis,  the  large  trans- 
former will  only  waste  ^  per  cent.  Let  the  large 
transformer  have  x  times  the  out-put  of  the  small 
one,  then  linear  dimensions  must  be  proportional 
to  x\.  Weight  and  cost  per  kilowatt  and  percen- 
tage loss  by  hysteresis  will  be  proportional  to  x$. 
This  calculation  neglects,  however,  the  working 
temperature  which,  for  obvious  reasons,  must  not 
exceed  a  certain  limit.  In  practice  it  is  found  that 
for  every  watt  lost  by  hysteresis,  eddy  currents,  and 
ohmic  resistance  a  cooling  surface  of  from  five  to 
ten  square  inches  must  be  provided.  As  the  larger 
transformer  has,  relatively  to  its  out-put,  a  smaller 
external  surface  than  the  smaller  transformer,  it  is 
not  possible  to  take  full  advantage  of  the  law  be- 
tween linear  dimensions  and  out-put  here  given. 
In  part,  owing  to  the  difficulty  of  heating,  we  very 
soon  arrive  at  a  limit  of  out-put  when  a  further 
increase  of  dimension  varies  the  out-put  scarcely 
faster  than  the  weight  and  cost.  Thus  in  practice 


104  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

it  is  found  that  although  a  transformer  of  12 
kilowatts  does  not  weigh  nearly  as  much  as  four 
transformers  of  3  kilowatts,  a  transformer  of  60 
kilowatts  weighs  and  costs  very  nearly  twice  as 
much  as  a  transformer  for  30  kilowatts. 


CHAPTER  VIII. 

CENTRAL   STATIONS    AND    DISTRIBUTION   OF    ALTER- 
NATING CURRENTS. 

The  principal  reason  for  the  use  of  alternating 
currents  in  connection  with  the  supply  of  light  from 
a  central  station  to  private  customers  is  that  in  con- 
sequence of  the  high  pressure  which  can  safely  be 
used  we  are  able  to  take  on  customers,  whether 
near  or  far,  and  thus  carry  on  the  business  of  light 
purveyors  on  a  larger  scale,  and  presumably  with 
a  greater  profit,  than  if  we  were  restricted  to  those 
customers  only  who  live  near  the  station.  In  a 
general  sense  this  argument  is  perfectly  sound,  but 
it  would  be  a  mistake  to  apply  it  indiscriminately 
and  say  that  in  all  cases  the  supply  by  means  of 
alternating  currents  is  preferable  to  that  by  con- 
tinuous currents.  Whether  an  engineer  has  to  de- 
sign works  himself,  or  merely  to  inspect  and  approve 
works  carried  out  by  others,  it  will  always  be  his 


106  ALTERNATING    CURRENTS   OF   ELECTRICITY. 

first  concern  to  see  that  the  works  shall  be  a  com- 
mercial success.  We  cannot  build  central  stations 
or  any  other  works  without  the  aid  of  the  financier, 
and  the  financier  cares  very  little  for  any  technical 
perfection ;  all  he  cares  for  is  that  the  work  should 
pay,  and  unless  the  engineer  can  give  him  that  as- 
surance he  will  not  co-operate.  Hence  it  is  the 
business  of  the  engineer  not  only  to  design  his 
works  so  as  to  be  technically  a  success,  but  also 
commercially. 

In  considering  the  relative  merits  of  the  two  sys- 
tems, we  must  take  into  account  a  variety  of  local 
circumstances,  some  of  which  not  only  are  beyond 
the  reach  of  mathematical  representation,  that  is, 
representation  by  concrete  figures  which  we  can  use 
in  our  calculation,  but  may  even  be  but  vaguely 
known  at  the  time  the  station  is  being  designed. 
For  instance,  the  number  of  lamps  which  will  be 
required  in  any  given  district,  the  daily  lighting 
time  of  each  lamp,  and  the  distribution  of  lamps 
between  the  different  classes  of  houses  in  the  dis- 
trict, are  matters  which  we  cannot  foretell  with  ab- 
solute certainty.  We  can  but  make  a  guess  based 
on  previous  experience.  Another  matter  of  some 


CENTRAL    STATIONS    AND    ALTERNATING    CURRENTS.     107 

importance,  but  about  which  it  is  extremely  diffi- 
cult to  form  an  estimate  beforehand,  is  the  danger 
of  being  served  with  an  injunction  for  noise  or 
vibration  by  some  of  the  kind  neighbours,  who  are 
always  on  the  look-out  how  to  make  a  little  money 
out  of  the  difficulty  of  others.  This  danger  is  evi- 
dently greater  in  the  direct  current  system,  because 
with  it  we  have  not  a  very  wide  choice  as  to  the 
position  of  our  station,  but  must  place  it  fairly  near 
to  and  preferably  in  the  centre  of  the  district  to 
be  lighted.  With  the  alternating  current  system 
we  can  afford  to  go  farther  afield  with  our  station, 
into  a  neighbourhood  the  inhabitants  of  which  are 
not  so  particular  as  to  noise  and  vibration.  Then 
there  is  the  question  of  the  total  extent  of  the  dis- 
trict to  be  lighted,  the  possibility  of  working  by 
water  power,  or  if  not,  the  cost  of  coal  and  water, 
the  quality  of  the  latter,  the  possibility  of  obtaining 
condensing  water,  and  many  other  points  which 
have  to  be  considered. 

If  we  have  to  do  with  a  compact  and  densely 
lighted  district,  where  most  of  the  lamps  can  be 
placed  within  a  few  hundred  yards  of  the  station 
(or  at  any  rate  within  a  radius  of  about  1,000 


108  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

yards),  then  the  direct  current  system  is  generally 
the  best.  One  of  its  greatest  advantages  lies  in  the 
fact  that  we  can  supplement  the  dynamos  by  storage 
batteries,  and  use  the  latter  during  the  hours  of 
minimum  demand.  For  economical  reasons  we 
are  obliged  to  use  compound  engines,  but,  as  you 
know,  a  compound  engine,  except  when  condens- 
ing, does  not  work  with  economy  when  lightly 
loaded,  and  it  is  therefore  advantageous  to  shut 
down  the  engines  altogether  in  the  early  hours  of 
the  morning  and  during  the  daytime,  putting  the 
batteries  on  for  the  supply  of  the  few  lamps  re- 
quired. In  this  respect  the  direct  current  has  a 
distinct  advantage,  but  this  advantage  becomes  less 
and  less  felt  as  the  total  power  of  the  station  is  in- 
creased, because  in  a  large  station  the  number  of 
lamps,  even  in  the  daytime,  will  be  large  enough 
to  fairly  load  a  small  engine,  and  if  we  can  obtain 
condensing  water  the  engine,  even  if  only  partly 
loaded,  will  work  with  fair  economy. 

A  point  at  present  in  favour  of  direct  currents  is 
the  ease  with  which  they  can  be  used  for  motive 
power,  but  there  is  every  prospect  that  ere  long 
alternate  current  motors  will  become  a  practical 


CENTRAL    STATIONS    AND    ALTERNATING    CURRENTS.     IOQ 

success.  At  any  rate,  the  use  of  motors  on  town 
circuits  has  with  us  not  yet  become  so  popular  that 
we  need  attach  any  great  weight  to  this  point.  The 
principal  advantage  of  the  alternating  current  sys- 
tem is  that  we  can  use  small  mains,  and  yet  keep 
the  pressure  throughout  the  district  very  nearly 
constant.  With  continuous  currents  not  only  do 
we  require  more  copper  in  the  mains  and  feeders, 
but  where  the  feeders  are  long,  the  loss  of  pressure 
in  them  amounts  sometimes  to  as  much  as  20  per 
cent,  of  the  total  or  station  voltage,  and  in  such 
cases  some  complicated  arrangements  are  required 
for  the  regulation  of  the  voltage,  so  as  to  keep  the 
pressure  at  the  feeding  centres  at  least  approxi- 
mately constant. 

There  are  two  ways  in  which  we  can  use  trans- 
formers. We  can  bring  the  high-pressure  mains 
right  into  the  house  of  each  customer  and  give  him 
his  own  little  transformer,  or  we  can  place  large 
transformers  at  certain  sub-stations,  and  lay  through 
the  streets  a  second  system  of  low-pressure  mains, 
with  house  connections,  in  the  same  way  as  if  the 
supply  were  by  direct  currents,  only  that  in  this 
case  the  low-pressure  mains  need  not  be  so  large, 


110  ALTERNATING    CURRENTS    OF   ELECTRICITY. 

since  we  can  put  down  as  many  sub-stations  as  we 
please,  and  thus  reduce  the  distance  to  the  lamps 
to  any  desired  limit.  The  system  of  a  separate 
transformer  for  each  customer  has  hitherto  been 
most  used,  but  it  is  not  the  best.  It  is  true  that  by 
it  we  save  the  cost  of  the  secondary  mains  and  the 
cost  of  the  sub-stations,  items  which  a  company  in 
its  early  pioneering  days,  when  customers  were  few 
and  far  between,  could  not  easily  afford.  On  the 
other  hand,  the  objections  to  the  use  of  separate 
transformers  are  great,  and  as  time  goes  on,  that 
is  to  say,  as  the  use  of  the  electric  light  extends, 
these  objections  acquire  additional  weight.  In  the 
first  place,  there  is  some  danger  in  having  a  high- 
pressure  apparatus  in  one's  house.  You  may  put 
your  transformer  into  the  cellar  in  a  fireproof  case 
and  lock  it  up,  but  when  you  have  thousands  of 
transformers  in  as  many  houses,  the  chances  are 
that  in  one  or  two  cases  the  locking  up  may  be  for- 
gotten, and  some  inquisitive  person  may  touch  a 
terminal.  A  further  objection  lies  in  this :  that  a 
number  of  small  transformers  cost  more  money  and 
waste  more  energy  than  one  large  transformer. 
Let  us  take  for  example  twenty  houses,  each  wired 


CENTRAL   STATIONS   AND    ALTERNATING   CURRENTS.    Ill 

for  fifty  lamps.  Each  house  must  get  its  so-light 
transformer.  The  whole  of  the  fifty  lamps  will 
not  be  lighted  simultaneously  every  day.  Probably 
not  more  than  half-a-dozen  times  in  the  year  will 
each  transformer  be  worked  at  its  full  out-put,  and 
there  is  the  hysteresis  loss  going  on  in  it  day  and 
night.  This  loss  means  waste  of  power  and  devel- 
opment of  heat ;  indeed,  I  have  heard  of  one  case 
in  which  the  heat  given  out  by  a  transformer 
placed  in  a  wine  cellar  was  sufficient  to  keep  the 
cellar  at  a  nice  even  temperature  all  the  year  round. 
General  experience  tells  us  that  scarcely  more  than 
J^,  or  at  most  60  per  cent.,  of  the  lamps  wired  in 
a  district  are  ever  alight  simultaneously.  The 
maximum  joint  demand  for  current  of  our  twenty 
houses  will  therefore  never  exceed  600  lamps,  and 
we  can  substitute  for  the  twenty  separate  trans- 
formers of  fifty  lights  each,  one  single  transformer 
of  600  lights.  From  what  I  have  said  before  about 
the  influence  of  size  on  the  cost  of  transformers, 
you  will  see  that  the  single  large  transformer  will 
cost  scarcely  more  than  a  third  the  money  required 
for  the  twenty  small  ones,  and  that  even  if  we  put 
down  two  large  transformers  so  as  to  keep  one  in 


112  ALTERNATING   CURRENTS   OF   ELECTRICITY. 

reserve,  we  shall  do  it  for  little  more  than  half  the 
money.  Similarly,  the  loss  of  power  by  hysteresis 
will  be  reduced  to  one  quarter,  and  this  is  a  very 
important  consideration.  Take  for  instance  a  sta- 
tion designed  for  20,000  lamps,  of  which  12,000 
will  be  alight  simultaneously  during  the  two  or 
three  hours  of  maximum  demand.  The  average 
lighting  time  of  each  lamp  fixed  is  in  London  about 
500  hours  per  annum.  If  we  allow  with  small 
transformers  a  loss  of  2  per  cent,  by  hysteresis,  the 
power  continuously  absorbed  by  all  the  transform- 
ers connected  to  the  central  station  will  be  equiva- 
lent to  that  required  by  400  lamps.  We  are  wast- 
ing, therefore,  day  and  night  current  which  could 
feed  400  lamps.  In  a  year  we  waste  not  less  than 
3,500,000  lamp  hours,  whereas  our  total  income 
from  the  20,000  lamps  is  only  10,000,000  lamp 
hours.  This  means  that  even  if  there  were  no 
other  sources  of  loss  we  would  have  to  send  out 
energy  from  our  station  representing  13,500,000 
lamp  hours,  but  we  could  only  get  paid  for  10,000,- 
ooo  lamp  hours.  This  is  only  74  per  cent,  effi- 
ciency. Now  suppose  we  use  sub-stations  and 
large  transformers,  the  hysteresis  loss  will  fall  to 


CENTRAL    STATIONS    AND    ALTERNATING    CURRENTS.     113 

i  per  cent. ,  and  the  efficiency  will  rise  to  over  90 
per  cent.  We  can  further  improve  the  efficiency 
by  putting  down  at  the  sub-station  not  one  trans- 
former only,  but  two  or  more  of  different  size,  and 
make  arrangements  for  the  insertion  or  withdrawal 
of  transformers  from  the  two  circuits  (the  high  and 
low-pressure  circuits),  in  accordance  with  the  de- 
mand for  current,  so  that  during  the  hours  of  light 
load  the  hysteresis  loss  will  only  take  place  in  the 
smallest  transformer  of  the  group.  Mr.  Ferranti, 
Mr.  Gordon  and  myself  have,  independently  of 
each  other,  devised  an  apparatus  which  switches  in 
and  takes  out  the  transformers  automatically. 

The  employment  of  large  transformers  at  sub- 
stations has  this  further  advantage:  that  the  total 
length  of  high-pressure  mains  is  thereby  consider- 
ably reduced,  and  that  there  are  no  branch  connec- 
tions on  these  mains.  We  are  thus  able  to  get 
higher  insulation.  You  know  that  an  insulation  of 
many  hundreds  of  megohms  per  mile  can  be  easily 
attained  in  a  continuous  cable,  but  after  the  cable 
has  been  laid,  and  branch  connections  have  been 
made,  the  insulation  is  much  lower,  the  reason 

being  that  at  every  joint  the  insulation  has  first  to 
8 


114  ALTERNATING    CURRENTS   OF   ELECTRICITY. 

be  stripped,  and  then  made  good  again.  Now  it  is 
one  thing  to  put  on  the  insulation  in  the  factory, 
where  every  precaution  can  easily  be  taken  to  en- 
sure perfect  work,  and  it  is  quite  another  thing  to 
do  the  same  kind  of  work  at  the  bottom  of  a  trench 
or  pit  in  the  street.  No  matter  how  careful  we  are, 
the  insulation  put  on  under  these  circumstances  can 
never  be  so  good  as  that  put  on  by  the  covering 
machines  in  the  cable  factory.  For  this  reason  a 
system  of  simple  mains  radiating  from  the  central 
stations  to  the  sub-stations  must  show  a  higher  in- 
sulation than  a  complicated  network  of  mains  cov- 
ering the  whole  district. 

I  have  given  you  here  the  main  reasons  for  the 
adoption  of  transforming  sub-stations  in  connection 
with  alternate  current  distribution,  but,  in  applying 
them  to  each  given  case,  you  must  not  forget  to 
take  into  account  the  commercial  element.  A  sys- 
tem of  working  may  be  scientifically  the  best,  and 
yet  not  the  best  financially.  Thus  the  system  gen- 
erally applied  at  the  present  time  in  London  in 
alternating  current  stations  is  that  of  a  separate 
transformer  for  every  customer,  not  because  it  is 
theoretically  the  best,  but  simply  because  it  is  com- 


CENTRAL   STATIONS   AND    ALTERNATING   CURRENTS.     115 

mercially  the  only  feasible  system.  I  have,  how- 
ever, no  doubt  that  as  the  use  of  the  light  becomes 
more  general,  the  various  companies  will  find  it 
advantageous  to  change  to  the  system  of  sub-sta- 
tions. I  have  hitherto  not  said  anything  as  to  the 
comparative  cost  of  continuous  and  alternate  cur- 
rent stations,  and  it  is  indeed  very  difficult  to  state 
it  in  any  definite  way.  The  cost  of  boilers,  en- 
gines, and  accessory  apparatus  will  be  about  the 
same  in  both  systems.  The  alternators  will  be  a 
little  cheaper  than  the  dynamos,  and  there  will 
also  be  the  cost  of  the  battery  against  the  continu- 
ous current  system.  On  the  other  hand,  we  have 
to  remember  that  the  whole  engine  power  may  be 
slightly  less,  since  during  the  hours  of  heavy  light- 
ing the  battery  assists  the  engines.  Taking,  then, 
one  thing  with  another,  there  will  not  be  any  very 
great  difference  in  the  cost  of  the  plant  at  the  cen- 
tral station  on  the  two  systems.  The  difference  is 
mostly  outside.  If  the  district  is  large,  the  extra 
cost  of  the  heavy  feeders  and  mains  will,  with  con- 
tinuous currents,  be  much  greater  than  that  of  the 
high-pressure  feeders  and  low-pressure  mains  if 
alternating  currents  are  used,  and  the  margin  left 


Il6  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

will  be  more  than  sufficient  to  pay  for  the  trans- 
formers at  the  sub-stations.  If  the  district  be 
small,  and  the  lighting  compact,  then  the  balance 
will  be  the  other  way.  The  cost  of  mains  will  be 
about  the  same  in  the  two  systems,  but  we  shall 
not  be  able  to  save  enough  on  the  cost  of  the  feed- 
ers to  pay  for  the  cost  of  the  transformers.  Each 
case  must,  in  fact,  be  judged  on  its  own  merits, 
and  what  I  have  said  here  about  comparative  cost 
is  merely  intended  as  a  guide  in  forming  such  a 
judgment. 


CHAPTER   IX. 

EXAMPLES   OF  CENTRAL   STATIONS. 

As  examples  to  illustrate  this  lecture,  I  choose 
three  types  of  central  stations,  distinguished  from 
each  other  mainly  by  the  character  of  the  motive 
power  employed.  In  the  first  type  the  motive 
power  is  steam,  in  the  second  it  is  water  power, 
and  in  the  third  it  is  electricity. 

I .  The  Sardinia  Street  Station  of  the  Metropolitan 
Electric  Supply  Company. — The  boilers  are  of  the 
Babcock  Wilcox  type,  and  placed  on  the  ground- 
floor.  The  battery  of  boilers  is  parallel  to  the  two 
rows  of  engines  in  the  adjoining  room,  also  on  the 
ground-floor,  but  at  a  slightly  higher  level.  This 
arrangement  of  boilers  and  engines  has  the  great 
advantage  of  reducing  the  length  of  steam-piping, 
and  minimizing  the  inconvenience  resulting  from 
a  failure  of  any  particular  length  of  steam-pipe. 

The  steam-pipe  forms  what  is  technically  termed 

117 


Il8  ALTERNATING    CURRENTS   OF    ELECTRICITY. 

a  ring  main,  and  valves  are  inserted  at  suitable 
points,  so  that  any  length  can  be  cut  out  without 
disturbing  the  supply  of  steam  through  the  rest  of 
the  piping.  Adjoining  the  boiler-room,  and  con- 
nected with  it  by  a  tram  line,  is  a  vast  underground 
coal  store;  a  very  admirable  arrangement,  espe- 
cially in  a  station  situated,  as  is  that  of  Sardinia 
Street,  in  a  district  where  coals  can  only  be  deliv- 
ered by  cart,  and  where,  consequently,  the  delivery 
may,  in  times  of  heavy  frost  or  fog,  be  interrupted 
for  some  days  or  weeks.  The  engines  are  of  the 
compound  high  speed  Westinghouse  type,  and 
drive  by  belt  Westinghouse  alternators  placed  on 
an  upper  floor.  Alongside  one  wall  of  the  machine- 
room  is  placed  the  switchboard,  by  means  of  which 
any  desired  combination  between  the  alternators 
and  external  circuits  can  be  quickly  made.  During 
the  hours  of  light  load  all  the  circuits  are  put  on  to 
one  or  two  machines,  but  as  the  load  increases 
other  machines  are  started,  and  some  of  the  cir- 
cuits are  transferred  to  them.  The  machines  are 
not  worked  in  parallel.  As  regards  the  mains,  I 
must  mention  an  ingenious  arrangement  due  to 
Mr.  Bailey,  the  engineer  to  the  company.  In 


EXAMPLES    OF    CENTRAL    STATIONS.  1 19 

order  to  avoid  trie  difficulties  connected  with  the 
insulation  of  joints,  when  these  are  made  in  the 
streets  Mr.  Bailey  makes,  as  far  as  possible,  all 
connections  of  the  high-pressure  mains  by  terminal 
blocks  on  the  customer's  premises.  Under  this 
arrangement  the  insulation  is  only  stripped  at  the 
ends  which  enter  the  terminals,  and  which  them- 
selves can  be  perfectly  insulated.  It  is  true  that 
under  this  arrangement  the  total  length  of  cable 
required  is  slightly  increased,  namely,  by  the  length 
of  the  bight  taken  into  each  house ;  but  this  is  only 
a  small  percentage  of  the  straight  run  of  main. 
Further,  we  have  the  advantage  that  each  house 
is,  so  to  speak,  served  by  duplicate  mains,  namely, 
one  on  either  side,  and  that,  therefore,  the  house 
need  not  be  cut  off  even  if  one  length  of  main  in 
the  street  should  for  any  reason  have  to  be  discon- 
nected. We  have  here,  in  fact,  the  electrical  equiv- 
alent of  the  ring  main  between  the  engines  and 
boilers. 

2.  The  Lynton  Station. — This  is  worked  by  water 
power  from  the  River  Lyn  on  a  fall  of  96  feet,  the 
water  being  supplied  to  the  turbine  through  a  30- 
inch  pipe.  Owing  to  the  high  fall  the  speed  is 


120  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

sufficient  for  driving  the  alternators,  which  are 
Mordey  machines  directly  coupled  one  on  either 
side  of  the  turbine.  Each  alternator  is  capable  of 
developing  37*5  kilowatts.  The  speed  is  regulated 
by  a  slide  valve  in  the  main  water  supply  pipe  worked 
by  a  hand-wheel.  The  mains  are  lead-covered  Cal- 
lender  bitumen  cables  laid  underground. 

3.  The  Keswick  Station. — This  is  also  worked  by 
water  power  obtained  from  the  River  Greta,  but 
since  the  fall  is  only  20  feet,   the  alternators  are 
driven  by  belt  from  the  turbine  shaft.     The  plant 
comprises  two    3O-kilowatt  Kapp   alternators,   the 
necessary  exciting  machine,  switchboards  and  in- 
struments, and  a  boiler  and  Westinghouse  engine 
to  serve  as  an  auxiliary  source  of  power  in  case  of 
drought  or  frost.     The  mains  are  insulated  cables 
placed  overhead  on  oil  insulators,  but  for  a  certain 
distance  they  had  to  be  taken  underground,  and 
then  a  Brookes'  pipe  line  is  used. 

4.  The  C asset  Station. — This  is  an  example  of  a 
central  station  where  the  motive  power  is  electricity. 
There  are  two  stations  in  the  town  in  which  dyna- 
mos  are    driven  by  Kapp  alternators  working  as 
motors.     The  alternating  current  is  supplied  from 


EXAMPLES   OF    CENTRAL    STATIONS. 


121 


a  water-power  station  four  miles  distant.  Fig.  29 
shows  the  arrangement  diagrammatically.  At  the 
power  station  a  turbine  drives  two  Kapp  alterna- 
tors, each  designed  to  give  30  amperes  at  2,200 


Op 

o 


D2         _J_ 


D3| —     — JD4 
J 


999 


FIG.  29. 

volts.  The  machines  are  coupled  in  parallel,  and 
the  current  is  taken  by  a  concentric  lead-covered 
cable  to  Cassel,  where  the  cable  splits  into  two 
branches  each  leading  to  a  lighting  station.  At 
each  of  these  lighting  stations  there  is  a  6o-kilo- 
watt  alternator  coupled  direct  to  two  3O-kilowatt 


122  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

dynamos  wound  for  1 10  volts,  one  dynamo  on  each 
side  of  the  alternator.  The  dynamos  are  arranged 
on  the  three-wire  system,  and  work  on  to  a  three- 
wire  network  common  to  both  stations.  At  one 
of  the  stations  there  is  also  a  battery  of  storage 
cells,  from  which  the  town  is  supplied  during  the 
hours  of  minimum  demand.  Towards  evening, 
when  it  is  necessary  to  supplement  the  batteries  by 
dynamo  power,  or  when  it  is  desired  to  re-charge 
the  batteries,  the  dynamos  are  switched  on  to  the 
network,  and  receive  current  from  it.  This  sets 
them  in  motion,  and,  working  for  the  time  being 
as  motors,  they  run  up  the  alternators  to  synchro- 
nizing speed.  The  alternating  current  is  then 
switched  on,  and  the  action  between  the  machines 
is  reversed,  the  alternators  acting  as  motors,  and 
driving  now  the  dynamos.  The  two  stations  sup- 
ply at  present  current  for  2,600  i6-candle-power 
lamps  burning  simultaneously,  or  3,500  lamps 
wired,  but  provision  has  been  made  to  extend  the 
plant,  so  as  to  eventually  supply  12,000  lamps 
wired. 


CHAPTER  X. 

PARALLEL  COUPLING  OF  ALTERNATORS. 

I  have  already  pointed  out  that  for  economical 
reasons  it  is  advisable  to  work  the  engines  at  a 
station  as  nearly  as  possible  at  their  full  load,  and 
you  will  easily  see  that  this  condition  can  most 
easily  be  fulfilled  if  the  alternators  can  be  worked 
in  parallel.  For  were  it  only  possible  to  work  each 
machine  quite  independently  of  the  other  machines, 
we  should  be  obliged  to  keep  a  larger  number  of 
machines  working  on  small  loads,  and  as  the  hours 
of  light  load  greatly  exceed  those  of  full  load,  the 
engines  would  be  used  under  very  uneconomical 
conditions.  But  if  we  can  couple  the  alternators 
parallel,  then  we  can  put  on  and  take  off  machines 
exactly  in  accordance  with  the  demand  for  current, 
and  have  our  engines  fairly  well  loaded  at  all  times. 
Some  years  ago  it  was  believed  that  alternators  had 

to  be  designed  specially  for  working  in  parallel, 

123 


124  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

and  certain  makers  claimed  this  quality  of  their 
machines  as  something  specially  in  their  favour. 
If  parallel  running  succeeded  it  was  put  down  to 
the  credit  of  the  particular  type  of  alternator ;  if  it 
failed  the  design  of  the  alternator  was  considered 
faulty.  It  is  only  recently  that  we  have  come  to 
recognize  that  the  real  difficulty  of  parallel  run- 
ning is  not  in  the  alternator  at  all,  but  in  the  en- 
gine. Any  alternators  when  driven  by  turbines 
which  have  an  absolutely  constant  angular  speed 
will  run  in  parallel  perfectly,  but  if  you  drive  the 
machines  from  slow  speed  steam  engines  by  means 
of  belts  or  ropes,  any  irregularity  in  the  angular 
speed  of  the  engines  is  magnified  by  reason  of  the 
multiplication  of  speed,  and  the  machine  becomes 
alternately  a  generator  and  a  motor,  the  transition 
from  one  state  to  the  other  being  accompanied 
by  heavy  mechanical  and  electrical  strains,  which 
render  anything  like  smooth  working  impossible. 
The  condition  of  successful  parallel  working  is, 
therefore,  a  direct-coupled  engine  having  a  very 
even  angular  speed.  This  is  a  point  of  great  prac- 
tical importance,  and  it  is  intimately  connected 
with  the  general  question  of  alternators  used  as 


PARALLEL   COUPLING    OF    ALTERNATORS.  125 

motors,  since  when  the  engine  fails  to  keep  up  its 
even  angular  speed  the  alternator  steps  in  and 
compels  it  to  do  so ;  it  acts,  in  fact,  for  a  moment, 
as  a  motor,  and  controls  the  engine. 


CHAPTER   XL 

ALTERNATING  CURRENT    MOTORS. 

When  investigating  the  transmission  of  power 
by  alternating  currents,  we  may  consider  the  cir- 
cuit as  consisting  of  three  parts :  a  line  having  a 
definite  resistance;  an  alternator  working  as  gen- 
erator at  one  end ;  and  another  alternator  working 
as  motor  at  the  other  end.  Such  a  conception 
would  be  the  most  obvious,  but  it  is  not  the  best, 
because  we  are  thereby  compelled  to  investigate 
simultaneously  the  behaviour  of  two  machines.  To 
simplify  the  treatment  I  shall  assume  the  following 
case : — Given  a  pair  of  terminals,  between  which  by 
some  means  we  maintain  a  constant  alternating 
electromotive  force  at  constant  frequency,  and  the 
source  from  which  this  electromotive  force  is  sup- 
plied shall  be  so  abundant  that  we  may  take  any 
amount  of  energy  from  the  terminals,  or  put  any 

amount  of  energy  into  them,  without  altering  in 

126 


ALTERNATING   CURRENT   MOTORS.  127 

any  way  either  the  pressure  or  the  frequency. 
Such  a  pair  of  terminals  would,  for  instance,  be  the 
omnibus  bars  at  a  central  station,  if  from  them  we 
supply  a  small  motor.  Suppose  the  motor  run  up 
to  synchronizing  speed,  and  then  switched  on  to 
the  omnibus  bars.  We  now  want  to  know  the  re- 
lation between  the  mechanical  power  obtained,  the 
current  through  the  armature,  and  the  strength  of 
field.  This  apparently  complex  problem  can  be 
solved  graphically  by  means  of  a  clock  diagram  in 
a  very  simple  manner. 

It  is  self-evident  that  we  can  only  obtain  power 
from  the  motor  if  it  runs  at  such  a  speed  that  the 
frequency  of  the  electromotive  force  developed  in 
its  armature  coils  is  exactly  the  same  as  that  of  the 
current  which  drives  it,  and  that  the  electromotive 
force  of  the  motor  must  be  opposed  to  the  current. 

We  must,  therefore,  at  first  employ  some  exter- 
nal source  of  power  to  run  the  motor  up  to  the 
proper  speed  before  switching  on.  But  how  are 
we  to  know  when  the  proper  speed  has  been  reached  ? 
No  tachometer  or  speed  counter  can  give  us  this  in- 
formation with  sufficient  accuracy,  especially  since 
there  may  be  slight  variations  in  the  frequency  of 


128 


ALTERNATING    CURRENTS   OF   ELECTRICITY. 


the  supply  current.  If  we  wish  to  put  two  alter- 
nators in  parallel,  we  also  must  know  exactly  when 
their  phase  and  frequency  coincide,  and  for  this 
purpose  we  use  an  instrument  called  a  "  synchro- 
nizer." It  consists  mainly  of  two  small  transform- 
ers (Fig.  30)  the  primaries  of  which  are  connected 


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p/WV— r  P/W-I 
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FIG.  30. 

to  the  terminals  of  the  two  alternators  which  are  to 
be  coupled  parallel.  Two  of  these  terminals  may, 
of  course,  be  permanently  connected,  as  shown  in 
the  figure,  but  the  other  two  must  only  be  con- 
nected by  the  switch  S  when  the  machines  are  in 
step.  The  secondaries  of  the  two  transformers  are 
connected  as  shown,  and  into  this  circuit  are  placed 
some  incandescent  lamps.  By  following  out  the 
connections  you  will  easily  see  that  if  the  two  ma- 


ALTERNATING    CURRENT    MOTORS.  129 

chines  are  in  opposite  phase,  that  is,  in  a  condition 
when  you  must  not  couple  them,  there  is  no  elec- 
tromotive force  on.  the  lamps,  but  that  when  the 
machines  are  in  the  same  phase,  or,  as  we  call  it, 
"instep,"  then  the  lamps  get  the  full  electromotive 
force  of  the  two  transformers  coupled  in  series. 
We  thus  know  that  when  the  lamps  are  dark  the 
machines  are  out  of  step,  and  when  they  light  up 
the  machines  are  in  step.  But  complete  darkness 
or  complete  brightness  can  only  occur  when  the 
frequencies  are  absolutely  the  same.  Generally, 
the  frequencies  will  be  different,  and  the  lamps 
will  flicker.  Thus,  suppose  one  machine  is  running 
at  its  normal  speed,  and  the  other  is  being  started 
up,  at  first  there  will  be  very  rapid  flickering  in  the 
lamps.  As  the  speed  of  the  second  machine  in- 
creases, the  flickering  becomes  less  rapid,  and  by  de- 
grees, namely,  as  the  speed  approaches  that  which  is 
required  for  synchronism,  there  appear  regular  beats 
in  the  light  of  the  lamps,  which  get  longer  and 
longer.  You  watch  your  opportunity,  and  throw 
the  switch  on  in  the  middle  of  a  beat  when  the 
lamps  are  alight.  The  machines  are  then  so  nearly 
in  the  right  step  that  the  first  rush  of  current  pulls 
9 


1 30  ALTERNATING   CURRENTS  OP   ELECTRICITY. 

them  dead  into  step,  and  they  remain,  as  it  were, 
interlocked  in  that  condition.  The  electrical  coup- 
ling is,  in  fact,  comparable  to  a  kind  of  interlocking, 
which  is  as  secure  as  if  the  two  armature  spindles 
were  connected  by  spur  gearing.  To  test  the  reli- 
ability of  this  electrical  interlocking,  I  have  run  a 
60  and  a  lo-kilowatt  alternator  in  parallel,  supply- 
ing the  power  from  two  independent  sources.  I 
have  then  cut  off  the  power  from  the  small  machine. 
It  ran  on  exactly  as  before.  Next,  I  put  a  load  on 
the  small  machine,  and  increased  it  to  25  horse- 
power; still  the  machine  ran  on.  I  left  the  load  on 
for  some  hours,  and  then  suddenly  withdrew  and 
again  put  on  a  large  portion  of  the  load,  but  the 
machine  kept  in  step.  There  is,  of  course,  for 
every  machine  a  certain  load  at  which  it  will  be 
torn  out  of  step,  just  the  same  as  there  is  for  every 
spur  wheel  a  load  which  will  strip  its  teeth.  In 
the  machine  with  which  I  experimented  it  should 
be  possible  to  break  down  the  synchronism  with  a 
load  of  about  30  horse-power,  that  is,  twice  the 
normal  load,  but  I  was  not  able  to  determine  the 
breaking  off  load  experimentally  because  the  belt 
by  which  power  was  taken  from  the  motor  began 


ALTERNATING   CURRENT   MOTORS.  131 

to  slip  at  25  horse-power.  The  machines  with 
which  I  experimented  were  of  my  own  type,  but, 
as  I  have  said  before,  there  is  no  particular  virtue 
in  the  design,  any  modern  alternator  with  a  smooth 
armature  core,  and  having  a  fair  efficiency,  will  be- 
have in  exactly  the  same  manner. 

Having  now  given  you  some  practical  results  of 
parallel  running  and  transmission  of  power,  I  must 
briefly  explain  the  theory  of  it.  Fig.  3 1  represents 
the  condition  of  a  machine  supplying  current  to  a 
non-inductive  resistance.  OB  is  the  electromotive 
force  which  it  would  at  its  then  excitation  give  on 
open  circuit,  AB  is  the  electromotive  force  required 
to  overcome  its  self-induction  with  the  current  it 
actually  gives,  AR  is  the  electromotive  force  re- 
quired to  overcome  the  armature  resistance,  and 
RO  is  the  electromotive  force  available  for  the  ex- 
ternal circuit.  If  in  a  central  station  we  have 
already  a  number  of  machines  running  in  parallel, 
OR  would  be  the  electromotive  force  on  the  omni- 
bus bars,  and  if  we  wish  to  switch  in  a  new  ma- 
chine we  would,  in  order  to  have  it  in  the  same 
condition  as  the  others,  excite  it  to  such  a  degree 
that  on  open  circuit  it  will  give  the  electromotive 


13* 


ALTERNATING    CURRENTS   OF    ELECTRICITY. 


force  OB.  We  run  the  machine  up  to  the  right 
frequency  and  switch  it  on.  For  the  sake  of  the 
present  investigation,  I  will  assume  the  new  ma- 
chine can  be  mechanically  geared  with  one  of  the 
other  machines  in  such  a  way  that  its  electromotive 
force  shall  lag  or  lead  in  comparison  with  the  om- 
nibus electromotive  force  by  any  desired  angle. 
Thus  in  Fig.  32  OR  represents  the  omnibus  electro- 


FIG.  31. 

motive  force,  and  OB  the  machine  electromotive 
force,  the  angle  between  the  two  being  ensured 
constant  by  the  mechanical  gearing.  By  drawing 
the  parallelogram  ORCB  we  find  the  resultant  elec- 
tromotive force  in  the  new  machine  OC,  and  this 
can  be  regarded  also  as  the  resultant  of  the  electro- 
motive force  of  self-induction  CD,  and  that  lost  in 
armature  resistance  OD.  If  we  regard  the  coefficient 


ALTERNATING    CURRENT    MOTORS.  133 

of  self-induction  constant,  then  the  angle  ?>,  which 
OD  makes  with  OC,  is  the  same  as  that  which  in 
Fig.  31  RA  makes  with  RB,  and  the  direction  of 
the  line  OD  in  Fig.  32  is  at  once  defined.  The 


FIG.  32. 

point  D  is  found  by  dropping  a  perpendicular  from 
C  on  this  line.  Since  OD  represents  the  electromo- 
tive force  used  up  in  resistance,  and  since  we  know 
the  resistance,  it  is  easy  to  calculate  the  current. 
We  know  then  the  direction  and  magnitude  of  the 
current  as  well  as  of  the  electromotive  force,  and 
we  can  find  the  work  done  by  the  machine.  For  this 
purpose  we  multiply  the  current  with  the  electromo- 


134  ALTERNATING    CURRENTS   OF   ELECTRICITY. 

tive  force,  and  with  the  cosine  of  the  angle  enclosed 
between  the  two  lines.  The  work  thus  found,  we 
mark  off  on  the  line  OB  or  its  prolongation .  Now  let 
us  shift  our  mechanical  gearing  and  find  in  the  same 
manner  the  current  and  work  for  a  different  angle 
between  the  omnibus  and  machine  electromotive 
force,  and  repeating  the  construction  for  various 
phase  angles,  we  obtain  the  curves  on  Fig.  33, 
which  show  current,  and  work  as  functions  of  the 
phase  angle.  The  outer  curve  on  the  left  repre- 


FIG.  33. 

sents  the  work  given  out  by  the  machine  when  its 
phase  angle  lags  from  O  to  about  180°,  the  inner 
curve  represents  the  work  absorbed  by  the  machine 
(when  working  as  motor)  when  its  phase  angle  lags 
from  1 80  to  360°.  The  curves  on  the  right  repre- 
sent similarly  the  work  given  to  or  taken  from  the 


ALTERNATING    CURRENT    MOTORS.  135 

omnibus  bars.  You  will  notice  that  about  half  of 
the  curves  are  dotted.  The  dotted  parts  refer  to 
an  unstable  condition  of  working,  and  the  diagram 
shows  at  a  glance  why  it  is  impossible  to  run  two  al- 
ternators in  series  if  they  are  independently  driven, 
that  is,  not  mechanically  geared  together,  as  I  have 
assumed  to  be  the  case  for  the  purpose  of  explaining 
how  this  diagram  is  obtained.  You  will  also  see 
that  a  moderate  difference  in  the  phase  angle  is 
sufficient  to  transform  the  machine  from  a  strong 
generator  into  a  strong  motor.  The  difference  of 
position  in  the  two  cases  is  about  90°,  but  you  must 
remember  that  the  diagram  represents  a  two-pole 
machine.  In  reality  the  machines  are  made  with 
many  more  poles,  and  the  angle  is  much  smaller. 
For  instance,  if  there  were  eighteen  poles  the  angle 
would  only  be  about  10°,  and  this  explains  why  it 
is  essential  for  parallel  working,  and  also  for  power 
transmission,  to  employ  engines  which  will  impart 
to  the  machines  an  almost  absolutely  constant  an- 
gular velocity. 


CHAPTER   XII. 

SELF-STARTING   MOTORS. 

From  what  I  have  here  said  you  will  conclude 
that  there  is  no  difficulty  in  transmitting  power  by 
a  single  alternating  current,  but  that  the  motor  is 
not  self-starting.  The  system  is  thus  encumbered 
by  the  necessity  of  providing  a  separate  machine 
and  some  storage  of  power  to  set  this  in  motion. 
The  most  convenient  way  is  to  use  the  exciter  for 
this  purpose,  and  drive  it  by  a  storage  battery. 
When  the  alternator  is  working  as  a  motor  it  drives 
its  own  exciter,  and  the  latter  may  at  the  same 
time  be  used  to  charge  the  battery  up  again  ready 
for  the  next  start.  The  complication  and  cost  of 
this  arrangement  are  not  very  serious  objections 
when  we  have  to  deal  with  large  powers,  but  for 
the  distribution  of  small  parcels  of  power  the  neces- 
sity of  providing  a  separate  exciter  and  a  storage 

battery,  in  addition  to  the  motor  proper,  is  a  fatal 

136 


SELF-STARTING    MOTORS.  137 

objection,  and  various  attempts  have  been  made  to 
design  a  self-starting  alternate  current  motor.  One 
of  these,  and  I  may  at  once  say  the  most  successful 
one,  is  due  to  Mr.  Zipernowsky,  whose  firm  (Ganz 
&  Co.,  of  Budapest)  showed  at  the  Frankfort  Exhi- 
bition several  of  these  machines  at  work.  In  the 
limited  time  at  my  disposal  I  cannot  attempt  to 
give  you  a  detailed  description  of  these,  nor  enter 
into  the  many  refinements  of  construction  which 
have  been  found  necessary  in  developing  the  ma- 
chine practically.  I  must  content  myself  to  give 
you  the  main  principle  of  it.  In  Fig.  34  M  is  a 
laminated  magnet  and  A  an  armature  wound  with 
a  single  coil,  the  ends  of  which  are  brought  to 
a  two-part  commutator.  It  is,  in  fact,  the  well- 
known  Siemens  shuttle  armature,  also  employed 
in  the  small  Griscom  motor,  and  the  apparatus,  as 
here  shown,  is  nothing  else  than  a  very  simple  form 
of  continuous  current  motor,  which  is  self-starting 
from  almost  any  position.  The  only  position  when 
the  motor  will  not  start  is  when  the  armature  is 
placed  so  that  the  brush  on  each  side  touches  both 
commutator  segments  at  once.  To  start  the  motor 
from  this  position,  it  is  of  course  necessary  to 


138 


ALTERNATING    CURRENTS    OF    ELECTRICITY. 


slightly  shift  the  brushes  to  one  side  or  the  other 
of  the  dead  centre.  From  what  I  have  said  in 
Chapter  I.,  you  will  easily  see  that  this  kind  of 


FIG.  34. 

motor  will  also  start  and  work  with  an  alternating 
current,  but  its  power  will  at  first  be  very  slight. 
Observe  now  what  happens  when  the  alternating 
current  is  switched  on  whilst  there  is  no  load  on 
the  motor.  It  will  start  and  gather  speed  as  all 
series  wound  motors  do.  If  the  current  were  con- 
tinuous, the  motor  would  very  soon  begin  to  race, 
but  with  an  alternating  current  this  cannot  happen, 
because  in  trying  to  get  up  a  racing  pace  the  arma- 
ture must  pass  through  that  speed  which  corre- 
sponds to  the  frequency  of  the  supply  current.  At 


SELF-STARTING    MOTORS.  139 

the  moment  when  this  happens,  the  reversal  of  cur- 
rent produced  by  the  commutator  coincides  exactly 
with  the  reversal  of  the  supply  current,  and  the  re- 
sult is  that  the  current  flowing  through  the  arma- 
ture does  not  any  more  change  its  direction.  The 
armature  has  virtually  been  transformed  into  a 
field  magnet,  excited  by  a  continuous  current,  and 
what  was  at  starting  the  field  magnet  has  now  be- 
come the  armature  of  an  ordinary  alternator.  The 
moment  when  the  machine  jumps  into  step  can  be 
easily  noticed  by  the  behaviour  of  the  brushes. 
At  starting  there  is  violent  sparking  and  a  peculiar 
noise.  As  the  machine  gathers  speed  the  sparking 
gets  less,  and  suddenly  there  is  a  kind  of  jerk, 
after  which  both  noise  and  sparking  cease  and  the 
load  may  be  put  on.  The  motor,  when  once  in 
step,  will  even  stand  a  considerable  overload. 


CHAPTER   XIII. 

MULTIPHASE   CURRENTS. 

The  motor  I  have  just  described  will  start  itself, 
but  it  will  not  start  with  a  load.  The  sparking  is 
also  an  objection  which  renders  the  machine  use- 
less for  flour  mills,  cotton  mills,  and  any  works 
where  an  explosion  may  be  caused  by  sparks.  We 
can  therefore  not  regard  this  motor  as  the  final  so- 
lution of  the  problem  of  transmitting  power  by 
alternating  currents,  but  must  look  for  the  solu- 
tion in  quite  another  direction.  This  direction  has 
been  first  indicated  by  Professor  Galileo  Ferraris, 
of  Turin,  some  six  years  ago.  Quite  independent 
of  Ferraris,  the  same  discovery  was  also  made  by 
Nikola  Tesla,  of  New  York ;  and  since  the  practical 
importance  of  the  discovery  has  been  recognized, 
quite  a  host  of  original  discoverers  have  come  for- 
ward, each  claiming  to  be  the  first.  With  these 

various  claims  we  need  not  concern   ourselves  at 

140 


MULTIPHASE   CURRENTS. 


141 


present.  I  will  merely  describe  the  apparatus  used 
by  Ferraris.  He  employed  two  vertical  coils  AB 
(Fig.  35)  set  at  right  angles  to  each  other,  and  a 
copper  cylinder  C  suspended  between  them.  Two 
alternating  currents  of  the  same  frequency,  but 
with  a  phase  difference  of  90  degrees,  were  sent 
though  the  two  circuits,  and  the  copper  cylinder 
was  thereby  set  in  rotation.  The  explanation  is  as 


FIG.  35. 

follows: — Each  coil  taken  by  itself  produces  an 
oscillating  magnetic  field,  the  lines  of  which  are  at 
right  angles  to  the  face  of  the  coil.  The  two  coils 
together  produce  a  resultant  .field  which  revolves 
round  the  vertical  axis  of  the  apparatus.  The  sur- 
face of  the  copper  cylinder  is  therefore  being  con- 


142  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

tinuously  cut  by  lines  of  force  as  they  sweep  round ; 
currents  are  induced  in  the  copper  which  by  Lenz's 
law  are  in  such  directions  as  to  resist  motion ;  and 
since  the  cylinder  is  freely  suspended,  its  endeavour 
to  resist  the  motion  of  the  field  results  in  its  being 
set  in  motion  itself. 

Experiment  Lantern  and  Model. — In  translating 
this  laboratory  experiment  into  practical  work  we 
must,  of  course,  make  many  alterations  and  im- 
provements. We  must,  for  one  thing,  employ  iron 
to  get  a  more  compact  and  a  stronger  apparatus. 
We  must  also  sub-divide  the  two  coils  in  order  to 
get  a  machine  which  will  run  at  a  moderate  speed, 
and  finally  we  must  substitute  for  the  plain  copper 
cylinder  an  armature  properly  wound.  A  machine 
designed  on  these  lines  will  be,  generally  speaking, 
a  great  improvement  on  the  original  apparatus,  but 
in  one  respect  it  will  not  be  so  good.  In  Fig.  35 
the  coils  are  at  right  angles,  and  the  currents  are 
at  right  angles.  As  you  have  seen  by  the  model, 
the  effect  of  this  combination  is  an  absolutely  con- 
stant magnetic  field  revolving  round  the  axis  with 
constant  speed.  But  if  we  split  up  the  two  coils 
into  a  number  of  sections,  and  wind  these  alter- 


MULTIPHASE   CURRENTS.  143 

nately  side  by  side  on  a  cylindrical  core,  as  we 
wind  a  Gramme  armature,  one  of  our  conditions, 
namely,  that  of  the  right  angular  position  of  the 
two  coils,  has  been  lost,  for  the  coils  are  now  very 
nearly  in  line  with  each  other  all  the  way  round, 
and  the  result  is  that  the  field  is  not  any  more  ab- 
solutely constant.  I  can  show  you  this  by  means 
of  the  model.  By  setting  the  cranks  at  the  wrong 
angle  you  see  immediately  that  the  vector  of  the 
resultant  field  is  no  longer  the  radius  of  a  circle, 
but  of  a  curve  resembling  an  ellipse.  To  find  the 
variation  in  the  strength  of  the  resultant  field  we 
need  only  draw  the  two  current  curves  and  add 
up  their  ordinates  as  I  showed  you  in  Chapter  I. 
If  you  do  this  you  will  find  that  the  maximum 
strength  of  the  field  is  about  40  per  cent,  greater 
than  its  minimum  value.  The  field  is  now  not 
only  a  rotating  one,  but  it  also  pulsates.  The  ro- 
tation is  what  we  want,  but  the  pulsation  is  objec- 
tionable, as,  in  consequence  of  it,  useless  currents 
are  made  to  circulate  in  the  armature  conductors, 
producing  heat  but  no  power.  It  is  the  great  merit 
of  Herr  von  Dobrowolsky  to  have  been  the  first 
to  clearly  recognize  this  defect  in  machines  based 


ALTERNATING   CURRENTS   OF   ELECTRICITY. 

he  Tesla- Ferraris  motor.  The  evil  once  un- 
derstood, a  remedy  was  soon  found.  Dobrowolsky 
adopted  three  currents  instead  of  two,  and  thus  re- 
duced the  pulsation  of  the  field  at  once  to  some- 
thing like  14  per  cent. ;  but  even  this  was  not  quite 
satisfactory.  He  went,  therefore,  a  step  further 
and  re-arranged  the  winding  of  the  field  in  such  a 
way  as  to  produce  the  effect  of  six  distinct  currents, 
though  still  only  using  three  wires  in  the  line  of 
transmission.  A  reference  to  Fig.  36  will  make 


this  clear.  Let  abc  represent  the  three  coils  of  a 
two-pole  drum  armature,  such,  for  instance,  as  the 
armature  of  a  Thomson- Houston  machine,  but  in- 
stead of  joining  the  coils  to  a  common  centre  and 
to  a  three-part  commutator,  as  is  done  in  this  type 


MULTIPHASE    CURRENTS.  145 

of  machine,  let  them  be  joined  as  shown,  and  let 
the  points  of  junction  ABC  be  three  contact  rings 
by  which  the  currents  are  received  from  the  line. 
According  to  Kirchoff's  law,  the  algebraical  sum 
of  the  three  currents  ABC  must  at  all  times  be 
ero,  for  if  this  were  not  the  case  there  would  be 
an  accumulation  of  electricity  in  the  machine 
which  is  obviously  impossible.  Any  of  the  cur- 
rents may  therefore  be  regarded  as  the  resultant  of 
the  other  two  currents.  Here  we  have  a  simple 
three-phase  winding  and  a  rotating  field,  the  pulsa- 
tions of  which  are  about  14  per  cent,  of  its  mini- 
mum strength.  Now  to  reduce  these  pulsations, 
Dobrowolsky  adopts  the  following  expedient.  In- 
stead of  bringing  the  junction  between  b  and  c  di- 
rect to  the  contact  ring  A,  he  attaches  to  the  junc- 
tion a  stouter  wire  and  winds  this  round  the 
armature  in  a  coil  placed  midway  between  b  and  c. 
Similarly  B  is  wound  so  as  to  split  up  the  phase 
difference  between  a  and  c,  and  C  is  wound  in  be- 
tween a  and  b.  We  have  now  six  coils  on  the 
armature,  but  only  half  the  former  phase  difference 
between  neighbouring  coils.  Fig.  37  shows  a  two- 
pole  armature  so  wound,  and  in  this  way  the  pulsa- 
10 


146 


ALTERNATING   CURRENTS   OF   ELECTRICITY. 


tion  is  reduced  to  about  4  per  cent.  Were  the 
winding  not  split  up  in  the  manner  shown,  the 
tendency  to  produce  fluctuations  in  the  strength  of 


FIG.  37. 

the  resultant  field  would  cause  currents  to  circulate 
in  the  induced  part  of  the  winding,  and  these  cur- 
rents would  prevent,  to  a  certain  extent,  the  fluctu- 
ations. But  as  they  must  necessarily  circulate  in 
coils  which  at  the  moment  cannot  contribute  any- 
thing to  the  torque  by  reason  of  their  position  at 
right  angles  to  the  resultant  field,  these  currents 
represent  simply  so  much  waste  of  power  by  ohmic 
resistance.  Hence  Dobrowolsky's  method  of  split- 
ting up  the  winding,  although  not  indispensable, 


MULTIPHASE   CURRENTS.  147 

is  a  useful  device  for  increasing  the  out-put  obtain- 
able from  a  given  mass  of  iron  and  copper,  and  for 
increasing  the  efficiency.  I  have  called  the  part  of 
the  motor  represented  by  Fig.  37  an  armature,  but 
this  was  merely  to  point  out  the  analogy  with  a 
Thomson- Houston  armature.  It  would  be  more 
correct  to  call  this  part,  which  receives  the  currents 
from  the  line,  the  field,  because  its  function  is  to 
produce  the  revolving  field.  The  armature  of  the 
machine  is  a  hollow  cylinder  of  laminated  iron, 
built  up  of  thin  plates  in  the  usual  way,  and  pro- 
vided with  a  winding  which  is  closed  on  itself.  To 
understand  the  principle  of  this  winding,  imagine 
a  Gramme  ring,  the  winding  of  which  is  altered  in 
the  following  way.  Instead  of  joining  the  inner 
end  of  each  coil  with  the  outer  end  of  the  next  coil, 
so  as  to  produce  a  spiral  winding,  let  the  two  ends 
of  each  coil  be  joined  together.  You  will  then 
have  covered  the  Gramme  core  with  a  number  of 
distinct  coils,  each  closed  on  itself.  Now  put  a 
field  magnet  into  the  inner  space  of  the  armature 
and  revolve  this  magnet.  The  poles  sweeping  past 
the  closed  coils  of  the  armature  will  create  in  them 
very  powerful  currents,  and  the  mechanical  reaction 


148  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

of  these  currents  on  the  poles  will  require  the  ap- 
plication of  a  considerable  twisting  couple  or  torque 
to  keep  up  even  a  moderate  speed.  You  can  test 
this  for  yourselves  very  easily  by  means  of  any 
continuous  current  dynamo.  Excite  its  field  sepa- 
rately, and  short-circuit  the  brushes  by  a  thick 
wire.  If  you  then  turn  the  armature  by  hand  you. 
will  find  that  even  exerting  considerable  force  it 
will  only  creep  round  slowly,  and  you  will  thus 
realize  how  a  great  torque  may  be  developed  by  a 
small  angular  speed  of  the  armature  in  relation  to 
the  field  magnet.  This  is  an  important  fact,  and 
helps  us  to  understand  two  things  in  connection 
with  rotary  field  motors.  The  first  is  that  the 
speed  of  such  a  motor  does  not  vary  much  when 
the  load  varies,  since  small  variations  of  the  rela- 
tive speed  between  field  and  armature  produce  large 
variations  in  the  torque ;  and  the  second  is  that  the 
torque  at  starting  is  very  large,  the  reason  being 
that  at  starting  the  relative  speed  between  arma- 
ture and  field  is  a  maximum.  It  is,  however,  neces- 
sary to  observe  here  that  to  get  this  large  torque, 
resistance  must  be  inserted  in  the  armature  circuit, 
for  were  this  not  done,  the  current  in  the  armature 


MULTIPHASE    CURRENTS.  149 

coils  would  be  so  strong  as  to  demagnetize  the  re- 
volving field,  thus  again  reducing  the  torque.  We 
may  now  go  back  to  Fig.  37,  and  see  how  this 
works  out  in  practice.  You  have  seen  how  a  three- 
phase  current  passing  through  the  winding  pro- 
duces a  sensibly  constant  field,  which  revolves 
round  the  centre  with  a  speed  corresponding  to 
the  frequency.  The  armature  surrounds  the  part 
shown  in  Fig.  37,  but  is  omitted  from  the  diagram. 
The  lines  of  the  field,  in  sweeping  past  the  arma- 
ture conductors,  create  in  them  very  strong  cur- 
rents, and  the  mechanical  reaction  between  these 
currents  and  the  lines  of  the  field  tends  to  rotate 
the  armature  with  great  force.  If  the  armature 
were  movable  it  would  thereby  be  set  in  rotation. 
But  in  the  particular  machine  I  am  describing,  the 
armature  is  fixed,  whilst  the  field  magnet,  that  is, 
the  part  shown  in  Fig.  37,  can  rotate.  We  have 
then  a  twisting  couple  between  the  armature  and 
field ;  the  armature  cannot  move,  and  therefore  the 
field  must  move.  Let  us  now  see  what  is  the  effect 
of  this  movement.  Say  that  the  direction  of  the  cur- 
rents is  such  as  to  produce,  when  the  central  part  of 
the  machine  is  at  rest,  a  clockwise  rotation  of  the 


150  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

lines  of  force.  The  speed  of  rotation  between  the 
lines  and  the  wires  corresponds,  of  course,  always  to 
the  frequency.  If  the  wires  are  stationary  the 
lines  revolve  in  relation  to  any  fixed  object  in  space 
(for  instance,  the  wires  of  the  armature)  with  the  full 
speed  given  by  the  frequency,  say,  for  instance, 
thirty  revolutions  per  second  if  the  frequency  is 
thirty  and  our  machine  is  wound  for  two  poles,  as 
shown  in  Fig.  37.  Each  wire  of  the  armature  will 
therefore  be  cut  thirty  times  by  a  north  field,  and 
thirty  times  by  a  south  field  in  each  second,  and 
the  torque  produced  will  set  the  central  drum  rotat- 
ing counter-clockwise.  Say,  for  instance,  that  the 
central  drum  runs  backwards  with  a  speed  of  twenty 
revolutions  per  second.  The  relative  speed  be- 
tween the  central  drum  and  the  lines  of  force  is,  of 
course,  still  thirty  revolutions  per  second,  but  of 
these  thirty  revolutions  twenty  revolutions  are  made 
up  by  the  backward  rotation  of  the  drum,  leaving 
only  ten  revolutions  of  forward  speed  for  the  lines 
of  force  in  relation  to  any  fixed  point  in  space. 
The  wires  of  the  armature  are  now  cut  only  ten 
times  per  second  by  a  north  field,  and  ten  times 
per  second  by  a  south  field.  If  we  allow  the  drum 


MULTIPHASE    CURRENTS.  151 

to  run  faster  still,  the  speed  of  cutting  lines  will  be 
still  further  reduced.  If,  for  instance,  the  central 
drum  is  so  lightly  loaded  that  it  can  acquire  a  speed 
of  twenty-nine  revolutions,  the  absolute  speed  of 
the  field  in  relation  to  the  armature  will  be  reduced 
to  one  revolution,  and  each  armature  wire  will  be 
cut  by  a  north  field  only  once  a  second,  and  by  a 
south  field  also  once  a  second.  You  see,  therefore, 
that  the  less  the  load  on  the  motor  the  faster  it  will 
run,  and  this  is  precisely  the  same  condition  as  ob- 
tains in  an  ordinary  continuous  current  motor.  At 
starting,  when  the  drum  is  at  rest,  we  have  the 
greatest  torque,  and  as  the  speed  increases  the 
torque  diminishes.  This  is  a  very  important  prop- 
erty cf  the  three-phase  motor,  since  in  consequence 
of  it  the  machine  not  only  becomes  a  self-starting 
motor,  but  one  which  will  start  with  a  large  load. 
How  large  the  starting  load  may  be  depends  on  the 
more  or  less  skilful  design  of  the  motor.  There 
are,  as  already  pointed  out,  certain  reactions  of  the 
armature  on  the  field  which  tend  to  decrease  the 
starting  torque,  but  the  subject  is  too  difficult  and 
intricate  to  be  treated  in  the  limited  time  at  my 
disposal.  I  have  merely  given  you  a  bare  outline 


152  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

of  the  action  of  this  class  of  machine,  so  that  you 
may  understand  in  a  general  way  the  principle  of 
working. 

The  difference  in  speed  of  the  drum  and  the  field 
is  technically  termed  the  magnetic  slip  of  the  mo- 
tor, and  you  will  easily  see  that,  to  obtain  a  small 
magnetic  slip,  and  therefore  a  close  approach  to  a 
constant  speed,  we  must  employ  an  armature  of 
small  resistance.  Here,  again,  there  is  a  close 
analogy  between  the  three-phase  motor  and  an  or- 
dinary continuous  current  motor  with  shunt  or  sepa- 
rately excited  magnets.  In  practice,  the  magnetic 
slip  need  never  exceed  10  per  cent.,  and  is  generally 
between  3  and  5  per  cent.  This  means  that  the 
speed  of  the  motor  only  varies  5  per  cent,  between 
full  load  and  no  load. 

In  the  machine  which  I  have  described  the  inner 
revolving  part  is  the  field  magnet,  but  you  will  easily 
understand  that  the  design  could  also  be  reversed 
by  making  the  outer  ring  the  fixed  field  magnet, 
and  the  inner  drum  the  revolving  armature.  This 
arrangement  is,  in  fact,  adopted  for  small  motors, 
because  in  this  way  we  avoid  altogether  the  neces- 
sity of  using  rubbing  contacts,  but  it  has  the  disad- 


MULTIPHASE    CURRENTS.  153 

vantage  of  increasing  the  loss  from  hysteresis.  I 
have  shown  you  that  the  speed  with  which  the  field 
sweeps  through  the  iron  of  the  armature  is  very 
small,  namely,  that  corresponding  to  magnetic  slip, 
whereas  the  speed  with  which  the  field  sweeps 
through  the  iron  of  the  field  magnet  is  that  due  to 
the  frequency,  or  about  twenty  times  as  great. 
The  hysteresis  loss  in  the  armature  is  therefore 
trifling  as  compared  with  that  of  the  field,  and  it  is 
obviously  of  advantage  to  have  less  iron  in  the 
field  than  in  the  armature,  which  is  done  by  mak- 
ing the  inner  drum  the  field,  and  the  outer  cylinder 
the  armature.  In  small  machines,  where  efficiency 
is  not  of  paramount  importance,  the  opposite  ar- 
rangement is  adopted,  because  of  its  greater  sim- 
plicity and  reduced  cost. 

The  three-phase  motor  has  several  advantages 
over  its  two  rivals,  the  ordinary  continuous  current 
motor  and  the  ordinary  alternate  current  motor, 
whilst,  in  a  certain  measure,  it  combines  the  good 
qualities  of  both.  It  is  better  than  the  continuous 
current  motor,  because  of  its  greater  simplicity. 
There  is  no  commutator,  and  there  are  no  brushes. 
There  can  be  no  sparking,  and  the  motor  may 


154  ALTERNATING    CURRENTS    OF    ELECTRICITY. 

therefore  safely  be  used  in  coal  mines  and  other 
places  where  a  machine  that  is  liable  to  sparking 
would  be  dangerous.  As  a  matter  of  fact;  Mr. 
Tesla  has  already  constructed  motors  for  coal-cut- 
ting machines.  Its  greater  simplicity,  and  more 
robust  construction,  renders  it  also  applicable  on 
board  ship  and  other  places  where  it  is  exposed  to 
rough  usage.  It  would,  for  instance,  be  perfectly 
feasible  to  design  a  three-phaser  which  will  stand 
being  drenched  with  sea- water,  and  yet  work  on  as 
if  nothing  had  happened.  Another  advantage  is 
that  the  distance  over  which  power  has  to  be  trans- 
mitted can  be  much  increased.  With  ordinary 
continuous  current  motors  this  distance  is  limited, 
because  we  cannot  make  such  machines,  especially 
if  of  small  power,  for  high  voltages.  With  a  three- 
phaser  there  is  no  such  narrow  limit  to  the  voltage, 
for  it  is  always  possible  to  work  through  transform- 
ers, raising  the  voltage  at  the  generating  station, 
and  letting  it  down  again  at  the  motor  station,  and 
this  can  be  done  with  very  small  loss.  Thus,  in 
the  Lauffen  transmission  of  power,  the  voltage  of 
the  generating  machine  was  only  50  volts  (meas- 
ured from  any  of  the  three  terminals  to  earth), 


MULTIPHASE    CURRENTS.  155 

whilst  the  voltage  of  any  line  wire  measured  in  the 
same  way  was  160  times  as  great  in  some  experi- 
ments, and  320  times  as  great  in  others. 

Ordinary  alternators  offer,  of  course,  the  same 
facility  of  transmitting  power  at  high  voltage  and 
utilizing  it  at  low  voltage,  but  they  do  not  offer  the 
same  facility  for  distributing  the  power  in  small 
parcels,  because  each  motor  must  be  provided  with 
some  source  of  independent  electrical  energy  for 
starting  and  field  excitation.  It  is  also  claimed  by 
Her  von  Dobrowolsky  that  the  total  weight  of  cop- 
per in  the  line  is  better  utilized  if  arranged  in  three 
wires  for  the  three-phase  current  than  in  two  wires 
for  a  single-phase  current,  but  on  this  point  I  can- 
not give  you  my  own  opinion,  as  I  have  not  yet  in- 
vestigated it.  One  of  the  objections  against  the 
three-phase  current  is  that  it  does  not  admit  of  a 
variable  speed  of  motor,  which,  for  many  purposes, 
especially  for  traction  work,  is  an  absolute  necessity. 
This,  no  doubt,  is  a  serious  drawback,  but  we  may 
reasonably  expect  that  the  men  who  have  succeeded 
in  transmitting  something  like  200  horse-power 
over  a  distance  of  1 10  miles  will,  in  time,  also  suc- 
ceed in  solving  this  problem. 


SHELL  TRANSFORMERS, 

OUTPUT  OF  ALL  6  K.  W. 


Plate  I 


Item,              96  Ibs". 

Iron,           100  Ibs. 
Copper,       340  " 

Copper^       450  u 
Hygferesisi     1,3* 

^—\ 

Hysteresis,     1.45$ 

Iron,  90  Ibs. 

Copper,      160  " 
Hysteresis 


Iron,  105  Ibs. 

Copper,        120  " 
Hysteresis, 


Iron, 

Copper, 

"Hysteresis, 


'102  IBs. 


Iron, 

Copper, 

Hysteresis, 


108  Ibs. 


Iron,  119  Ibs. 

Copper,         54  w 
Hysteresis,. 


Iron,  154  Ibs. 

Copper,         25  " 
JHysteresis,    2.2* 


SHELL  TRANSFORMERS. 

OUTPUT  OF  ALL  6  K.  W. 

jtebH        TLEOFFEEr\        i. 


Iron,  94  Ibs. 

Copper,       116  " 
Hysteresis,     1.3# 


Plate 


Iron,  105  Ibs. 

Copper,          93  " 
Hysteresis,      1.53* 


Iron,  103  Ibs. 

Copper,         59  " 
Hysteresis,     1.55* 


Iron,  114  Ibs. 

Copper,         48  " 
Hysteresis,     1.7* 


D     D 


Iron,  120  Ibs. 

Copper,         33  " 
'Hysteresis,     1..7W 


Iron,  115  Ibs. 

Copper,        19  " 
'Hysteresis, 


Irpn,  135  Ibs. 

Copper,         27  " 
Hysteresis,     1.94j< 


Iron,  173  Ibs. 

Copper,         15  " 
Hysteresis,      2.5556 


INDEX. 


AIR-GAP,  Resistance   of,    diminished  with  iron    arma- 
tures, 80 
Alternators,  Advantages  of,  80 

compared  with  continuous  current  machines, 

62 

Conductors  of,  74 
Coreless,  79 
Cores  of,  74 
Description  of,  82 
Design  of,  71,  74 
in  parallel,  128 

Experiment  with,  130 
in  series,  135 

Mechanical  construction  of,  73 
Practical  forms  of,  62,  63 
Simple  form  of,  59 

Alternators,  Brown's  three-phase,  74,  80 
Ferranti,  79-82 
Kapp,  87 
Kennedy,  89 
Kingdon,  88 
Lowrie-Hall,  65 
Meritens,  79 

159 


160  .  INDEX. 

Alternators,  Mordey,  79,  84 
Siemens,  79 
Thomson-Houston,  85 
Westinghouse,  65,  85 
Alternating  current  machines,  57 

motors,  126 

Alternating  currents,  Clock  diagram  of,  18 
Combining,  20 
described,  11 
Distribution  of,  105 
Graphical  representation  of,  15 
Sinusoidal  curve  of,  16 
Zeuner  diagram  of,  19 
Ampere-balance,  Thomson's,  39 
Armatures,  Advantage  of  iron  cores  in,  80 
Alternating  machine,  65-74 
Coreless,  79 

Losses  by  hysteresis  in,  78 
of  three-phase  motors,  147 
Split  up,  to  avoid  eddy  currents,  83 
with  no  wire,  88 
Average  volts  and  current,  40,  45 

AILEY'S  system  of  mains,  118 

Blakesley,  37,  41 
Brown,  C.  E.  L.,  6 

Three-phase  machine  of,  74,  80 


C 


ENTRAL  STATION,  Cassel,  122 
Keswick,  120 
Lynton,  119 
Sardina  St.,  Met.  E.  S.  Co.,  117 


INDEX.  l6l 

Central  stations,  105 

Alternating  vs.  continuous  current,  107,  115 
Choking  coil,  15 
Coefficient  of  E.  M.  F.  of  alternator,  71 

Numerical  values  of,  72,  88 
of  self-induction,  28,  35 
Clock  diagram,  of  alternating  currents  and  E.  M.  F.,  18 

Motor,  127 

Commutator,  Advantage  of  absence  of,  in  alternators,  80 
Conductors  of  alternators,  74 
Construction,  Mechanical,  of  alternators,  73 

Precautions  necessary  in,  74 
Cooling  surface  of  transformers,  103 
Core  transformers,  98 
Cores  of  alternators,  74 
Current,  Average,  40,  45 
Effective,  39,  45 
Work  of,  46 

Currents,  Alternating,  explained,  u 
Conventional  view  of,  9 
Direction  of  flow  of,  10 
Quarter-phase,  5 
Three-phase,  5 
Curve,  Sinusoidal,  16 

Trapezoidal,  of  E.  M.  F.,  68 

DESIGN  of  alternators,  71,  73,  74 
Dobrowolski,  6 

motor,  143 

EDDY  currents,  Cure  for,  74 
Losses  from,  reduced,  83 
Thomson,  Elihu,  on,  75 
ii 


162  INDEX. 

Effective  currents  and  E.  M.  F.,  39 

determined  analytically,  44,  45 
determined  graphically,  67 
E.  M.  F.,  Average,  40,  44 

Coefficient  of,  71,  72 
Counter,   53 

and  self-inductive,  Relation  between,  54 
Curve  of,  actual,  69 

sinusoidal,  16 
trapezoidal,  68 
Effective,  39,  45>  6l>  62 
Expression  of,  for  alternators,  7  1 
Factors  of,  of  alternators,  70,  71 
Formula  of  maximum,  61 
of  self-induction,  28,  53 
Ewing,  76 


alternator,  79,  82 
Ferraris,  Prof.  Galileo,  140 

Motor  model  of,  141 
Field,  Intensity  of,  60 

Strength  of,  in  Mordey  alternator,  85 
Fleming,  34 
Frequency,  14,  20,  53,  61 

Effect  on  motor  of  lowering,  55 


motor,  55 


HEAT  developed  a  measure  of  E.  M.  F.  and  current,  66 
Hysteresis,  73,  76 

How  to  reduce  loss  from,  77 


INDEX.  163 

Hysteresis,  Losses  from,  76,  99,  101,  103,  in,  153 
Loss  in  kilo-watts,  78 

INDUCTANCE,  32 

*     Induction  and  current  curve,  25 

Change  of,  25 

Coefficient  of  self-,  28,  35 

Total,  6 1 

Instantaneous  values  of  current  and  E.  M.  F.,  28,  29 
Impedance,  34 

KAPP  alternator,  87,  121,  122 
Kelly,  6 

Kennedy  alternator,  89 
Kingdon  alternator,  88 

LAG  of  E.  M.  F.,  29,  32 
Angle  of,  33,  43 
Lines  of  force,  24 

MAGNET  poles  of  alternators,  64,  65 
Influence   of,  on  shape  of  curve   of  E. 

M.  F.,  65,  66 
Lowrie-Hall  type  of,  65 
Mordey  form  of,  84 
should  be  of  equal  strength,  83 
Westinghouse  type  of,  65 
Magnetic  friction  or  hysteresis,  76 
leakage,  95 

Effect  of,  96 
slip,  152 
Measurement  of  pressure,  current  and  power,  37 


164  INDEX. 

Meri ten's  alternator,  79,  84 
Mordey  alternator,  79,  84 
Motor,  Dobrowolski,  144 
Ganz,  55 

Tesla-F'erraris,  143,  154 
Zipernowsky,  137 
Motors,  Alternating  current,  52-55,  126 

Effect  of  lower  frequency  on,  55 

Multiphase,  141 

Self-starting,  136,  151 

Starting,  55,  122 

Theory  of  alternating,  131 

Three-phase,  140 

Two-phase,  140 
Motor-transformer,  92 
Multiphase  currents,  140 

PARALLEL  coupling  of  alternators,  123 

Theory  of,  131 
Period  of  current,  53 
Permeability,  25 
Phase,  20 

Angle  of,  133 
Power,  maximum,  Analytical  deduction  of,  56 

Condition  of,  49 

Graphical  representation  of,  51 
Pulsation  of  multiphase  current  field,  143,  145,  146 

UARTER-PHASE  currents,  5 


p  OTARY  field,  Action  of,  148 


INDEX.  165 

SELF-INDUCTION,  24,  26,  27,  29,  50 
Coefficient  of,  28,  35 

E.  M.  F.  of,  28,  53 

Phenomena  of,  30 
Self-starting  motors,  136 
Shell  transformers,  98 
Siemens  alternator,  79 

dynamometer,  39,  40,  43 

Sinusoidal  curve  of  alternating  currents  and  E.  M.  F.,  16 
Stanley,  Wm.,  Jr.,  3-6 
Steinmetz,  6 

Storage  battery  for  starting  motors,  136 
Sub-stations,  Transforming,  109,  114 
Swineburne's  hedgehog  transformer,  97 
Synchronizer,  128 


TESLA  motor,   143,  154 
Nikola,  140 

Thomson's  ampere-balance,  39 
Thomson,  Elihu,  on  eddy  currents,  75 

experiments  with  armature  coils,  86 
Thomson-Houston  alternator,  86 
Three-phase  alternator,  74 
currents,  5 
motors,  144 

Advantages  of,  153 
Objections  to,  155 
Transformers,  91 

Core,  98 
Hedgehog,  97 
Magnetic  leakage  in,  95 
Motor-  92 


1 66  INDEX. 

Transformers,  Principles  of,  92,  99 

Relation  between  dimensions  of,  101 
Shell,  98 

Small  vs.  large,  109,  113 
Temperature  of,  103 
Transforming  ratio  of,  95 
Variation  of  E.  M.  F.  in,  94,  97 

Transforming  sub-stations,  109 

Transmission  of  power,  Theory  of,  131 

Two-phase  motors,  140 

motor  model,  141 


V 


OLTMETER,  Cardew,  39,  66 

Copper-electrolysis,  40 

Correction    of  readings  of,   with  alternating 

currents,  37,  42 
measures  heat  developed,  66 

WATTMETER,  43 
Correction  for,  48 
Theory  of,  47 

Watts,  apparent  and  true,  42,  46 
Westinghouse  alternator,  85,  118 

'TEUNER  diagram  of  alternating  currents  and  E.  M.  F., 

L,    I9 

Zipernowsky  motor,  137 


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In  the  words  of  the  author  "The  motive  of  this 
publication  has  been  that  I  have  understood  that  one 
or  two  of  these  papers  are  out  of  print  and  not  so  acces- 
sible to  American  readers  as  an  author  who  very  greatly 
values  the  good  opinion  of  American  electrical  engi- 
neers would  desire. " 

Copies  of  this  or  any  other  electrical  book  or  books  pub- 
lished, will  be  promptly  mailed  to  any  address  in  the  world, 
POSTAGE  PREPAID,  on  receipt  of  price.  Address 

The  W,  J.  JOHNSTON  COMPANY,  Ld,, 

TIMES  BUILDING,  NEW  YORK. 


The  Electric  Railway 

IN  THEORY  AND  PRACTICE.  ' 

By  O.  T.  CROSBY  and  Dr.  LOUIS  BELL. 

Second  Edition.    Revised  and  Enlarged. 

410  Octavo  Pages,  182  Illus.    Price,  $2. BO. 

This   is    the  first   SYSTEMATIC    TREATISE  that  has 
been  published  on  the  ELECTRIC  RAIL  WAY,  and 
it  is  intended  to  cover  Ihe  GENERAL  PRIN- 
CIPLES OF  DESIGN,  CONSTRUC- 
TION AN  JO  OPERATION. 

XABUG  OK  CONTENTS : 

Chapter    I.  General  Electrical  Theory. 

II.  Prime  Movers. 

"        III.  Motors  and  Car  Equipment. 

IV.  The  Line. 

V.  Track,  Car  Houses,  Snow  Machines. 

1         VI.  The  Station. 

VII.  The  Efficiency  of  Electric  Traction. 

VIII.  Storage  Battery  Traction. 

IX.  Miscellaneous  Methods  of  Electric  Traction. 

X.  High  Speed  Service. 

"         XI  Commercial  Considerations. 

u       XII.  Historical  Notes. 

APPENDICES: 

Appendix  A.    Electric  Railway  vs.  Telephone  Decisions. 

B.  Instructions  to  Linemen. 

C.  Engineer's  Log  Book. 

"          D.     Classification  of  Expenditures  of  Electric  Street 

Railways. 
'•  E.     Concerning      Lightning    Protection,      by      Prof 

Elihu  Thomson. 
"          F.    Motors  with  Beveled   Gear,  and    Series  Multiple 

Control  of  Motors. 
44          G.    Method    of  Measuring  Insulation    Resistance    of 

Overhead  Lines, 

Copies  of  this  or  any  other  Electrical  Book  or  Books 
published,  will  be  promptly  mailed  to  any  address  in  the 
world)  POSTAGE  PREPAID,  on  receipt  of  price.  Address 

Tfce  W.  J.  JOHSTOJ*  CO  , 

TIMES  BUILDING,  NEW  YORK. 


RECENT  PROGRESS 


IN 


ELECTRIC    RAILWAYS 

BEING  A  SUMMARY  OF  CURRENT  PROGRESS 

IN  ELECTRIC  RAILWAY  CONSTRUCTION, 

OPERATION,  SYSTEMS,  MACHINERY, 

APPLIANCES,  &c.,  COMPILED 

By  CARL    HERINC. 

386  pages  and  120  illustrations.    Cloth,        -        Price,  $1.00 


This  volume  contains  a  classified  summary  of  the 
recent  literature  on  this  active  and  promising  branch 
of  electrical  progress,  with  descriptions  of  new  appa- 
ratus and  devices  of  general  interest. 


CONTENTS. 

Chapter  I.— Historical.  Chapter  II.-— Development 
and  Statistics.  Chapter  III.— Construction  and  Opera- 
tion. Chapter  IV.— Cost  of  Construction  and  Opera- 
tion. Chapter  V. — Overhead  Wire  Surface  Roads. 
Chapter  VI. — Conduit  and  Surface  Conductor  Roads. 
Chapter  VII.— Storage  Battery  Roads.  Chapter  VIII. 
— Underground  Tunnel  Roads.  Chapter  IX.  -High 
Speed  Interurban  Railroads.  Chapter  X.—  Miscellan- 
eous Systems.  Chapter  XI.— Generators,  Motors  and 
Trucks.  Chapter  XII. — Accessories. 

Copies  of  this  or  any  other  electrical  book  or  books  pub- 
lished, will  be  promptly  mailed  to  any  address  in  the  world, 
POSTAGE  PREPAID,  on  receipt  of  price.  Address 

The  W.  J.  JOHNSTON  COMPANY,  Ld., 

TIMES  BUILDING,  NEW  YORK. 


THE  PIONEER  ELECTRICAL  JODRNAL  OF  AMERICA. 


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